From 1b0c42f08af68f397d5caeeaf8fdc8290d6ec06a Mon Sep 17 00:00:00 2001
From: Christophe Geuzaine <cgeuzaine@ulg.ac.be>
Date: Thu, 15 Mar 2018 17:38:47 +0100
Subject: [PATCH] use DOS end of lines
---
CircuitCoupling/RLC_circuit.geo | 66 +-
CircuitCoupling/RLC_circuit.pro | 730 +++++++--------
CircuitCoupling/RLC_circuit_common.pro | 24 +-
CircuitCoupling/R_circuit.geo | 78 +-
CircuitCoupling/R_circuit.pro | 684 +++++++-------
CircuitCoupling/R_circuit_common.pro | 30 +-
Elasticity/wrench2D.geo | 144 +--
Elasticity/wrench2D.pro | 731 ++++++++-------
Elasticity/wrench2D_common.pro | 58 +-
Electrostatics/microstrip.geo | 116 +--
Electrostatics/microstrip.pro | 651 +++++++-------
Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro | 936 ++++++++++----------
Magnetodynamics/electromagnet.geo | 108 +--
Magnetodynamics/electromagnet.pro | 178 ++--
Magnetodynamics/electromagnet_common.pro | 8 +-
Magnetodynamics/transfo.geo | 346 ++++----
Magnetodynamics/transfo.pro | 518 +++++------
Magnetodynamics/transfo_common.pro | 98 +-
Magnetostatics/electromagnet.geo | 108 +--
Magnetostatics/electromagnet.pro | 534 +++++------
Magnetostatics/electromagnet_common.pro | 8 +-
PotentialFlow/magnus.geo | 142 +--
PotentialFlow/magnus.pro | 849 +++++++++---------
PotentialFlow/magnus_common.pro | 54 +-
PotentialFlow/nacaAirfoil.geo | 444 +++++-----
Thermics/brick.geo | 222 ++---
Thermics/brick.pro | 906 ++++++++++---------
Thermics/brick_common.pro | 74 +-
28 files changed, 4415 insertions(+), 4430 deletions(-)
diff --git a/CircuitCoupling/RLC_circuit.geo b/CircuitCoupling/RLC_circuit.geo
index 2bb9299..cd10b79 100644
--- a/CircuitCoupling/RLC_circuit.geo
+++ b/CircuitCoupling/RLC_circuit.geo
@@ -1,33 +1,33 @@
-// Just 3 cubes
-
-Include "RLC_circuit_common.pro";
-
-lc = 0.25; // Characteristic length
-
-Point(1) = {0, 0, 0, lc};
-Extrude {1, 0, 0} {
- Point{1};
-}
-Extrude {0, 1, 0} {
- Line{1};
-}
-Extrude {0, 0, 1} {
- Surface{5};
-}
-Translate {2, 0, 0} {
- Duplicata { Volume{1}; }
-}
-Translate {4, 0, 0} {
- Duplicata { Volume{1}; }
-}
-
-Physical Surface(Cube1Top) = {27};
-Physical Surface(Cube1Bottom) = {5};
-Physical Surface(Cube2Top) = {34};
-Physical Surface(Cube2Bottom) = {29};
-Physical Surface(Cube3Top) = {61};
-Physical Surface(Cube3Bottom) = {56};
-
-Physical Volume(Cube1) = {1};
-Physical Volume(Cube2) = {28};
-Physical Volume(Cube3) = {55};
+// Just 3 cubes
+
+Include "RLC_circuit_common.pro";
+
+lc = 0.25; // Characteristic length
+
+Point(1) = {0, 0, 0, lc};
+Extrude {1, 0, 0} {
+ Point{1};
+}
+Extrude {0, 1, 0} {
+ Line{1};
+}
+Extrude {0, 0, 1} {
+ Surface{5};
+}
+Translate {2, 0, 0} {
+ Duplicata { Volume{1}; }
+}
+Translate {4, 0, 0} {
+ Duplicata { Volume{1}; }
+}
+
+Physical Surface(Cube1Top) = {27};
+Physical Surface(Cube1Bottom) = {5};
+Physical Surface(Cube2Top) = {34};
+Physical Surface(Cube2Bottom) = {29};
+Physical Surface(Cube3Top) = {61};
+Physical Surface(Cube3Bottom) = {56};
+
+Physical Volume(Cube1) = {1};
+Physical Volume(Cube2) = {28};
+Physical Volume(Cube3) = {55};
diff --git a/CircuitCoupling/RLC_circuit.pro b/CircuitCoupling/RLC_circuit.pro
index ff8fae3..9f76616 100644
--- a/CircuitCoupling/RLC_circuit.pro
+++ b/CircuitCoupling/RLC_circuit.pro
@@ -1,365 +1,365 @@
-/* -------------------------------------------------------------------
- Tutorial 8b : circuit coupling - RLC circuit
-
- Features:
- - Electrokinetic formulation coupled with RLC circuit
- - Transient resolution
-
- To compute the solution in a terminal:
- getdp RLC_circuit -solve dynamic -pos Cube_Top_Values_ASCII
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > RLC_circuit.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-/*
- This example shows how to implement a circuit with discrete resistors,
- capacitors, inductors, voltage- and current-sources in a transient finite
- element simulation. There are three separate cubes, each with a certain
- conductivity. The bottom of all cubes is kept at 0V via the constraint
- Voltage_3D. The cubes are connected according the `RLC_circuit.jpg` schematic.
-*/
-
-Include "RLC_circuit_common.pro";
-
-// FEM domain group data
-Group {
- // Surfaces
- Top1 = Region[Cube1Top];
- Bottom1 = Region[Cube1Bottom];
- Top2 = Region[Cube2Top];
- Bottom2 = Region[Cube2Bottom];
- Top3 = Region[Cube3Top];
- Bottom3 = Region[Cube3Bottom];
-
- // Volumes
- Cube1 = Region[Cube1];
- Cube2 = Region[Cube2];
- Cube3 = Region[Cube3];
-
- // FEM Electrical regions
- // * all volumes
- Vol_Ele = Region[{Cube1, Cube2, Cube3}];
- // * all surfaces connected to the lumped element circuit
- Sur_Ele = Region[{Top1, Bottom1, Top2, Bottom2, Top3, Bottom3}];
- // * total electrical computation domain
- VolWithSur_Ele = Region[{Vol_Ele, Sur_Ele}];
-}
-
-// Circuit group data - Fictive regions for the circuit elements
-Group {
-
- // Sources
- CurrentSource1 = Region[{3001}];
- VoltageSource1 = Region[{3002}];
-
- // Resistors
- R1 = Region[{4001}];
- R2 = Region[{4002}];
-
- // Inductors
- L1 = Region[{4003}];
-
- // Capacitors
- C1 = Region[{4004}];
-
- Resistance_Cir = Region[{R1, R2}]; // All resistors
- Inductance_Cir = Region[{L1}]; // All inductors
- Capacitance_Cir = Region[{C1}]; // All capacitors
- SourceI_Cir = Region[{CurrentSource1}]; // All current sources
- SourceV_Cir = Region[{VoltageSource1}]; // All voltage sources
-
- // Complete circuit domain containing all circuit elements
- Domain_Cir = Region[{Resistance_Cir, Inductance_Cir, Capacitance_Cir,
- SourceI_Cir, SourceV_Cir}];
-}
-
-Function {
- // Simulation parameters
- tStop = 10.0e-6; // Stop time [s]
- tStep = 100e-9; // Time step [s]
- nStrobe= 1; // Strobe periode for saving the result
-
- SaveFct[] = !($TimeStep % nStrobe); // Only each nStrobe-th time-step is saved
-
- // FEM domain function data
- // ------------------------
-
- Vbottom = 0.0; // Absolute voltage at the bottom of all cubes
-
- // Geometry of a cube
- w = 1.0; // Width [m]
- l = 1.0; // Length [m]
- h = 1.0; // Height [m]
-
- // Resistance
- Rcube1 = 10.0; // Resistance of cube 1 [Ohm]
- Rcube2 = 40.0; // Resistance of cube 2 [Ohm]
- Rcube3 = 20.0; // Resistance of cube 3 [Ohm]
-
- // Specific electrical conductivity [S*m/m^2]
- kappa[Cube1] = h / (w * l * Rcube1);
- kappa[Cube2] = h / (w * l * Rcube2);
- kappa[Cube3] = h / (w * l * Rcube3);
-
- // Circuit domain function data
- // ----------------------------
-
- // Resistors
- R[R1] = 30.0; // Resistance of R1 [Ohm]
- R[R2] = 40.0; // Resistance of R2 [Ohm]
-
- // Inductors
- L[L1] = 100.0e-6; // Inductance of L1 [H]
-
- // Capacitors
- C[C1] = 250.0e-9; // Capacitance of C1 [F]
-
- // Note: All voltages and currents are assigned / initialized in the
- // Constraint-block
-}
-
-// FEM domain constraint data
-Constraint {
- { Name Current_3D ; Type Assign ;
- Case {
- }
- }
- { Name Voltage_3D ; Type Assign ;
- Case {
- { Region Bottom1; Type Assign; Value Vbottom; }
- { Region Bottom2; Type Assign; Value Vbottom; }
- { Region Bottom3; Type Assign; Value Vbottom; }
- }
- }
-}
-
-// Circuit domain constraint data
-Constraint {
- { Name Current_Cir ;
- Case {
- { Region CurrentSource1; Type Assign; Value 1.0; } // CurrentSource1 has 1.0 A
- { Region L1; Type Init; Value 1.0; } // Initial current of L1 is 1.0 A
- }
- }
- { Name Voltage_Cir ;
- Case {
- { Region VoltageSource1; Type Assign; Value 80.0; } // VoltageSource1 has 80.0 V
- { Region C1; Type Init; Value 0.0; } // Initial voltage of C1 = 0.0 V
- }
- }
-
- { Name ElectricalCircuit ; Type Network ;
- Case Circuit1 {
- // Circuit for cube 1:
- { Region VoltageSource1; Branch{ 1, 10};}
- { Region R1; Branch{ 1, 2};}
- // The voltage between nodes 2 and 3 corresponds to the absolute voltage
- // of the surface Top1:
- { Region Top1; Branch{ 2, 3};}
- // Note the reverse order of the nodes in the next branch: it's for
- // subtracting the bottom voltage.
- { Region Bottom1; Branch{ 10, 3};}
- // With the two lines above, the voltage between node 2 and 10 corresponds
- // to the voltage drop over the cube regardless what the absolute voltages
- // are. The current between node 2 and 3 corresponds to the absolute
- // current flowing through Top1. The same is valid for Bottom1. Due to the
- // reverse order here the current has the opposite sign. This is correct
- // because the current flowing IN Top1 is flowing OUT of Bottom1. Note
- // that in this particular circuit it is actually not necessary to include
- // the bottom faces in the netlist, because all bottoms are kept at 0 V
- // via constraint Voltage_3D... But then all Bottom faces have to be
- // excluded also in the region Sur_Ele!
-
- // Circuit for cube 2:
- { Region L1; Branch{ 4, 10};}
- { Region R2; Branch{ 4, 10};}
- { Region Top2; Branch{ 4, 5};}
- { Region Bottom2; Branch{10, 5};}
-
- // Circuit for cube 3
- { Region CurrentSource1; Branch{ 6, 10};}
- { Region C1; Branch{ 6, 10};}
- { Region Top3; Branch{ 6, 7};}
- { Region Bottom3; Branch{10, 7};}
- }
- }
-}
-
-Jacobian {
- { Name JVol ;
- Case {
- { Region Region[{Vol_Ele}]; Jacobian Vol; }
- { Region Region[{Sur_Ele}]; Jacobian Sur; }
- }
- }
-}
-
-Integration {
- { Name I1 ;
- Case {
- { Type Gauss ;
- Case {
- { GeoElement Point ; NumberOfPoints 1 ; }
- { GeoElement Line ; NumberOfPoints 5 ; }
- { GeoElement Triangle ; NumberOfPoints 6 ; }
- { GeoElement Quadrangle ; NumberOfPoints 7 ; }
- { GeoElement Tetrahedron ; NumberOfPoints 15 ; }
- { GeoElement Hexahedron ; NumberOfPoints 34 ; }
- { GeoElement Prism ; NumberOfPoints 21 ; }
- }
- }
- }
- }
-}
-
-FunctionSpace {
- // Function space for the FEM domain
- { Name Hgrad_V; Type Form0;
- BasisFunction {
- // All nodes but the grouped nodes of the surfaces for connecting the
- // circuitry
- { Name sn; NameOfCoef vn; Function BF_Node;
- Support VolWithSur_Ele; Entity NodesOf[ All, Not Sur_Ele ]; }
- // Grouped nodes: Each surface of Sur_Ele has just one single voltage
- { Name sf; NameOfCoef vf; Function BF_GroupOfNodes;
- Support VolWithSur_Ele; Entity GroupsOfNodesOf[ Sur_Ele ]; }
- }
- GlobalQuantity {
- { Name U; Type AliasOf; NameOfCoef vf; }
- { Name I; Type AssociatedWith; NameOfCoef vf; }
- }
- Constraint {
- { NameOfCoef vn; EntityType NodesOf ; NameOfConstraint Voltage_3D; }
- { NameOfCoef U; EntityType GroupsOfNodesOf ; NameOfConstraint Voltage_3D; }
- { NameOfCoef I; EntityType GroupsOfNodesOf ; NameOfConstraint Current_3D; }
- }
- }
-
- // Function space for the circuit domain
- { Name Hregion_Cir; Type Scalar;
- BasisFunction {
- { Name sn; NameOfCoef ir; Function BF_Region;
- Support Domain_Cir; Entity Domain_Cir; }
- }
- GlobalQuantity {
- { Name Iz; Type AliasOf; NameOfCoef ir; }
- { Name Uz; Type AssociatedWith; NameOfCoef ir; }
- }
- Constraint {
- { NameOfCoef Uz ; EntityType Region ; NameOfConstraint Voltage_Cir ; }
- { NameOfCoef Iz ; EntityType Region ; NameOfConstraint Current_Cir ; }
- }
- }
-
-}
-
-
-Formulation {
- { Name dynamic; Type FemEquation;
- Quantity {
- { Name V; Type Local; NameOfSpace Hgrad_V; }
- { Name U; Type Global; NameOfSpace Hgrad_V [U]; }
- { Name I; Type Global; NameOfSpace Hgrad_V [I]; }
- { Name Uz; Type Global; NameOfSpace Hregion_Cir [Uz]; }
- { Name Iz; Type Global; NameOfSpace Hregion_Cir [Iz]; }
- }
- Equation {
- // FEM domain
- Galerkin { [ kappa[] * Dof{d V}, {d V} ]; In Vol_Ele;
- Integration I1; Jacobian JVol; }
- GlobalTerm{ [ Dof{I}, {U} ]; In Sur_Ele; }
-
- // Circuit related terms
- // Resistance equation
- GlobalTerm{ [ Dof{Uz}, {Iz} ]; In Resistance_Cir; }
- GlobalTerm{ [ R[] * Dof{Iz}, {Iz} ]; In Resistance_Cir; }
-
- // Inductance equation
- GlobalTerm{ [ Dof{Uz}, {Iz} ]; In Inductance_Cir; }
- GlobalTerm{ DtDof[ L[] * Dof{Iz}, {Iz} ]; In Inductance_Cir; }
-
- // Capacitance equation
- GlobalTerm{ [ Dof{Iz}, {Iz} ]; In Capacitance_Cir; }
- GlobalTerm{ DtDof[ C[] * Dof{Uz}, {Iz} ]; In Capacitance_Cir; }
-
- // Inserting the network
- GlobalEquation { Type Network; NameOfConstraint ElectricalCircuit;
- { Node {I}; Loop {U}; Equation {I}; In Sur_Ele; }
- { Node {Iz}; Loop {Uz}; Equation {Uz}; In Domain_Cir; }
- }
- }
- }
-}
-
-Resolution {
- { Name dynamic;
- System {
- { Name A; NameOfFormulation dynamic; }
- }
- Operation {
- InitSolution[A];
- TimeLoopTheta[0.0, tStop, tStep, 1.0]{
- Generate[A];
- Solve[A];
- Test[SaveFct[]] { SaveSolution[A]; }
- }
- }
- }
-}
-
-PostProcessing {
- { Name Ele; NameOfFormulation dynamic;
- Quantity {
- { Name V; Value{ Local{ [ {V} ]; In Vol_Ele; Jacobian JVol;} } }
- { Name Jv; Value{ Local{ [ -kappa[]*{d V} ]; In Vol_Ele; Jacobian JVol;} } }
- { Name J; Value{ Local{ [ Norm[kappa[]*{d V}] ]; In Vol_Ele; Jacobian JVol;} } }
- { Name U; Value { Term { [ {U} ]; In Sur_Ele; } } }
- // The minus sign here is for getting positive currents at the top of the
- // cubes. This is because incomming currents are negative.
- { Name I; Value { Term { [ -{I} ]; In Sur_Ele; } } }
- }
- }
-}
-
-PostOperation {
- // Absolute voltage everywhere [V]
- { Name V; NameOfPostProcessing Ele;
- Operation {
- Print[ V, OnElementsOf Vol_Ele, TimeLegend, File "Result_V.pos"];
- }
- }
- // Current through the top surfaces of the cubes [A]
- { Name I_Top; NameOfPostProcessing Ele;
- Operation {
- Print[ I, OnElementsOf Region[{Top1, Top2, Top3}], TimeLegend,
- File "Result_I_Top.pos"];
- }
- }
- // Current density vectors everywhere [A/m^2]
- { Name J_vectors; NameOfPostProcessing Ele;
- Operation {
- Print[ Jv, OnElementsOf Vol_Ele, TimeLegend, File "Result_J_vectors.pos"];
- }
- }
- // Magnitude of current density everywhere [A/m^2]
- { Name J_magnitude; NameOfPostProcessing Ele;
- Operation {
- Print[ J, OnElementsOf Vol_Ele, TimeLegend, File "Result_J.pos"];
- }
- }
- // Store the results in an ASCII file
- { Name Cube_Top_Values_ASCII; NameOfPostProcessing Ele;
- Operation {
- Print[U, OnRegion Top1, File "Result_Cube1TopValues.txt", Format TimeTable];
- Print[U, OnRegion Top2, File "Result_Cube2TopValues.txt", Format TimeTable];
- Print[U, OnRegion Top3, File "Result_Cube3TopValues.txt", Format TimeTable];
-
- Print[I, OnRegion Top1, File > "Result_Cube1TopValues.txt", Format TimeTable];
- Print[I, OnRegion Top2, File > "Result_Cube2TopValues.txt", Format TimeTable];
- Print[I, OnRegion Top3, File > "Result_Cube3TopValues.txt", Format TimeTable];
- }
- }
-
-}
+/* -------------------------------------------------------------------
+ Tutorial 8b : circuit coupling - RLC circuit
+
+ Features:
+ - Electrokinetic formulation coupled with RLC circuit
+ - Transient resolution
+
+ To compute the solution in a terminal:
+ getdp RLC_circuit -solve dynamic -pos Cube_Top_Values_ASCII
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > RLC_circuit.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+/*
+ This example shows how to implement a circuit with discrete resistors,
+ capacitors, inductors, voltage- and current-sources in a transient finite
+ element simulation. There are three separate cubes, each with a certain
+ conductivity. The bottom of all cubes is kept at 0V via the constraint
+ Voltage_3D. The cubes are connected according the `RLC_circuit.jpg` schematic.
+*/
+
+Include "RLC_circuit_common.pro";
+
+// FEM domain group data
+Group {
+ // Surfaces
+ Top1 = Region[Cube1Top];
+ Bottom1 = Region[Cube1Bottom];
+ Top2 = Region[Cube2Top];
+ Bottom2 = Region[Cube2Bottom];
+ Top3 = Region[Cube3Top];
+ Bottom3 = Region[Cube3Bottom];
+
+ // Volumes
+ Cube1 = Region[Cube1];
+ Cube2 = Region[Cube2];
+ Cube3 = Region[Cube3];
+
+ // FEM Electrical regions
+ // * all volumes
+ Vol_Ele = Region[{Cube1, Cube2, Cube3}];
+ // * all surfaces connected to the lumped element circuit
+ Sur_Ele = Region[{Top1, Bottom1, Top2, Bottom2, Top3, Bottom3}];
+ // * total electrical computation domain
+ VolWithSur_Ele = Region[{Vol_Ele, Sur_Ele}];
+}
+
+// Circuit group data - Fictive regions for the circuit elements
+Group {
+
+ // Sources
+ CurrentSource1 = Region[{3001}];
+ VoltageSource1 = Region[{3002}];
+
+ // Resistors
+ R1 = Region[{4001}];
+ R2 = Region[{4002}];
+
+ // Inductors
+ L1 = Region[{4003}];
+
+ // Capacitors
+ C1 = Region[{4004}];
+
+ Resistance_Cir = Region[{R1, R2}]; // All resistors
+ Inductance_Cir = Region[{L1}]; // All inductors
+ Capacitance_Cir = Region[{C1}]; // All capacitors
+ SourceI_Cir = Region[{CurrentSource1}]; // All current sources
+ SourceV_Cir = Region[{VoltageSource1}]; // All voltage sources
+
+ // Complete circuit domain containing all circuit elements
+ Domain_Cir = Region[{Resistance_Cir, Inductance_Cir, Capacitance_Cir,
+ SourceI_Cir, SourceV_Cir}];
+}
+
+Function {
+ // Simulation parameters
+ tStop = 10.0e-6; // Stop time [s]
+ tStep = 100e-9; // Time step [s]
+ nStrobe= 1; // Strobe periode for saving the result
+
+ SaveFct[] = !($TimeStep % nStrobe); // Only each nStrobe-th time-step is saved
+
+ // FEM domain function data
+ // ------------------------
+
+ Vbottom = 0.0; // Absolute voltage at the bottom of all cubes
+
+ // Geometry of a cube
+ w = 1.0; // Width [m]
+ l = 1.0; // Length [m]
+ h = 1.0; // Height [m]
+
+ // Resistance
+ Rcube1 = 10.0; // Resistance of cube 1 [Ohm]
+ Rcube2 = 40.0; // Resistance of cube 2 [Ohm]
+ Rcube3 = 20.0; // Resistance of cube 3 [Ohm]
+
+ // Specific electrical conductivity [S*m/m^2]
+ kappa[Cube1] = h / (w * l * Rcube1);
+ kappa[Cube2] = h / (w * l * Rcube2);
+ kappa[Cube3] = h / (w * l * Rcube3);
+
+ // Circuit domain function data
+ // ----------------------------
+
+ // Resistors
+ R[R1] = 30.0; // Resistance of R1 [Ohm]
+ R[R2] = 40.0; // Resistance of R2 [Ohm]
+
+ // Inductors
+ L[L1] = 100.0e-6; // Inductance of L1 [H]
+
+ // Capacitors
+ C[C1] = 250.0e-9; // Capacitance of C1 [F]
+
+ // Note: All voltages and currents are assigned / initialized in the
+ // Constraint-block
+}
+
+// FEM domain constraint data
+Constraint {
+ { Name Current_3D ; Type Assign ;
+ Case {
+ }
+ }
+ { Name Voltage_3D ; Type Assign ;
+ Case {
+ { Region Bottom1; Type Assign; Value Vbottom; }
+ { Region Bottom2; Type Assign; Value Vbottom; }
+ { Region Bottom3; Type Assign; Value Vbottom; }
+ }
+ }
+}
+
+// Circuit domain constraint data
+Constraint {
+ { Name Current_Cir ;
+ Case {
+ { Region CurrentSource1; Type Assign; Value 1.0; } // CurrentSource1 has 1.0 A
+ { Region L1; Type Init; Value 1.0; } // Initial current of L1 is 1.0 A
+ }
+ }
+ { Name Voltage_Cir ;
+ Case {
+ { Region VoltageSource1; Type Assign; Value 80.0; } // VoltageSource1 has 80.0 V
+ { Region C1; Type Init; Value 0.0; } // Initial voltage of C1 = 0.0 V
+ }
+ }
+
+ { Name ElectricalCircuit ; Type Network ;
+ Case Circuit1 {
+ // Circuit for cube 1:
+ { Region VoltageSource1; Branch{ 1, 10};}
+ { Region R1; Branch{ 1, 2};}
+ // The voltage between nodes 2 and 3 corresponds to the absolute voltage
+ // of the surface Top1:
+ { Region Top1; Branch{ 2, 3};}
+ // Note the reverse order of the nodes in the next branch: it's for
+ // subtracting the bottom voltage.
+ { Region Bottom1; Branch{ 10, 3};}
+ // With the two lines above, the voltage between node 2 and 10 corresponds
+ // to the voltage drop over the cube regardless what the absolute voltages
+ // are. The current between node 2 and 3 corresponds to the absolute
+ // current flowing through Top1. The same is valid for Bottom1. Due to the
+ // reverse order here the current has the opposite sign. This is correct
+ // because the current flowing IN Top1 is flowing OUT of Bottom1. Note
+ // that in this particular circuit it is actually not necessary to include
+ // the bottom faces in the netlist, because all bottoms are kept at 0 V
+ // via constraint Voltage_3D... But then all Bottom faces have to be
+ // excluded also in the region Sur_Ele!
+
+ // Circuit for cube 2:
+ { Region L1; Branch{ 4, 10};}
+ { Region R2; Branch{ 4, 10};}
+ { Region Top2; Branch{ 4, 5};}
+ { Region Bottom2; Branch{10, 5};}
+
+ // Circuit for cube 3
+ { Region CurrentSource1; Branch{ 6, 10};}
+ { Region C1; Branch{ 6, 10};}
+ { Region Top3; Branch{ 6, 7};}
+ { Region Bottom3; Branch{10, 7};}
+ }
+ }
+}
+
+Jacobian {
+ { Name JVol ;
+ Case {
+ { Region Region[{Vol_Ele}]; Jacobian Vol; }
+ { Region Region[{Sur_Ele}]; Jacobian Sur; }
+ }
+ }
+}
+
+Integration {
+ { Name I1 ;
+ Case {
+ { Type Gauss ;
+ Case {
+ { GeoElement Point ; NumberOfPoints 1 ; }
+ { GeoElement Line ; NumberOfPoints 5 ; }
+ { GeoElement Triangle ; NumberOfPoints 6 ; }
+ { GeoElement Quadrangle ; NumberOfPoints 7 ; }
+ { GeoElement Tetrahedron ; NumberOfPoints 15 ; }
+ { GeoElement Hexahedron ; NumberOfPoints 34 ; }
+ { GeoElement Prism ; NumberOfPoints 21 ; }
+ }
+ }
+ }
+ }
+}
+
+FunctionSpace {
+ // Function space for the FEM domain
+ { Name Hgrad_V; Type Form0;
+ BasisFunction {
+ // All nodes but the grouped nodes of the surfaces for connecting the
+ // circuitry
+ { Name sn; NameOfCoef vn; Function BF_Node;
+ Support VolWithSur_Ele; Entity NodesOf[ All, Not Sur_Ele ]; }
+ // Grouped nodes: Each surface of Sur_Ele has just one single voltage
+ { Name sf; NameOfCoef vf; Function BF_GroupOfNodes;
+ Support VolWithSur_Ele; Entity GroupsOfNodesOf[ Sur_Ele ]; }
+ }
+ GlobalQuantity {
+ { Name U; Type AliasOf; NameOfCoef vf; }
+ { Name I; Type AssociatedWith; NameOfCoef vf; }
+ }
+ Constraint {
+ { NameOfCoef vn; EntityType NodesOf ; NameOfConstraint Voltage_3D; }
+ { NameOfCoef U; EntityType GroupsOfNodesOf ; NameOfConstraint Voltage_3D; }
+ { NameOfCoef I; EntityType GroupsOfNodesOf ; NameOfConstraint Current_3D; }
+ }
+ }
+
+ // Function space for the circuit domain
+ { Name Hregion_Cir; Type Scalar;
+ BasisFunction {
+ { Name sn; NameOfCoef ir; Function BF_Region;
+ Support Domain_Cir; Entity Domain_Cir; }
+ }
+ GlobalQuantity {
+ { Name Iz; Type AliasOf; NameOfCoef ir; }
+ { Name Uz; Type AssociatedWith; NameOfCoef ir; }
+ }
+ Constraint {
+ { NameOfCoef Uz ; EntityType Region ; NameOfConstraint Voltage_Cir ; }
+ { NameOfCoef Iz ; EntityType Region ; NameOfConstraint Current_Cir ; }
+ }
+ }
+
+}
+
+
+Formulation {
+ { Name dynamic; Type FemEquation;
+ Quantity {
+ { Name V; Type Local; NameOfSpace Hgrad_V; }
+ { Name U; Type Global; NameOfSpace Hgrad_V [U]; }
+ { Name I; Type Global; NameOfSpace Hgrad_V [I]; }
+ { Name Uz; Type Global; NameOfSpace Hregion_Cir [Uz]; }
+ { Name Iz; Type Global; NameOfSpace Hregion_Cir [Iz]; }
+ }
+ Equation {
+ // FEM domain
+ Integral { [ kappa[] * Dof{d V}, {d V} ]; In Vol_Ele;
+ Integration I1; Jacobian JVol; }
+ GlobalTerm{ [ Dof{I}, {U} ]; In Sur_Ele; }
+
+ // Circuit related terms
+ // Resistance equation
+ GlobalTerm{ [ Dof{Uz}, {Iz} ]; In Resistance_Cir; }
+ GlobalTerm{ [ R[] * Dof{Iz}, {Iz} ]; In Resistance_Cir; }
+
+ // Inductance equation
+ GlobalTerm{ [ Dof{Uz}, {Iz} ]; In Inductance_Cir; }
+ GlobalTerm{ DtDof[ L[] * Dof{Iz}, {Iz} ]; In Inductance_Cir; }
+
+ // Capacitance equation
+ GlobalTerm{ [ Dof{Iz}, {Iz} ]; In Capacitance_Cir; }
+ GlobalTerm{ DtDof[ C[] * Dof{Uz}, {Iz} ]; In Capacitance_Cir; }
+
+ // Inserting the network
+ GlobalEquation { Type Network; NameOfConstraint ElectricalCircuit;
+ { Node {I}; Loop {U}; Equation {I}; In Sur_Ele; }
+ { Node {Iz}; Loop {Uz}; Equation {Uz}; In Domain_Cir; }
+ }
+ }
+ }
+}
+
+Resolution {
+ { Name dynamic;
+ System {
+ { Name A; NameOfFormulation dynamic; }
+ }
+ Operation {
+ InitSolution[A];
+ TimeLoopTheta[0.0, tStop, tStep, 1.0]{
+ Generate[A];
+ Solve[A];
+ Test[SaveFct[]] { SaveSolution[A]; }
+ }
+ }
+ }
+}
+
+PostProcessing {
+ { Name Ele; NameOfFormulation dynamic;
+ Quantity {
+ { Name V; Value{ Local{ [ {V} ]; In Vol_Ele; Jacobian JVol;} } }
+ { Name Jv; Value{ Local{ [ -kappa[]*{d V} ]; In Vol_Ele; Jacobian JVol;} } }
+ { Name J; Value{ Local{ [ Norm[kappa[]*{d V}] ]; In Vol_Ele; Jacobian JVol;} } }
+ { Name U; Value { Term { [ {U} ]; In Sur_Ele; } } }
+ // The minus sign here is for getting positive currents at the top of the
+ // cubes. This is because incomming currents are negative.
+ { Name I; Value { Term { [ -{I} ]; In Sur_Ele; } } }
+ }
+ }
+}
+
+PostOperation {
+ // Absolute voltage everywhere [V]
+ { Name V; NameOfPostProcessing Ele;
+ Operation {
+ Print[ V, OnElementsOf Vol_Ele, TimeLegend, File "Result_V.pos"];
+ }
+ }
+ // Current through the top surfaces of the cubes [A]
+ { Name I_Top; NameOfPostProcessing Ele;
+ Operation {
+ Print[ I, OnElementsOf Region[{Top1, Top2, Top3}], TimeLegend,
+ File "Result_I_Top.pos"];
+ }
+ }
+ // Current density vectors everywhere [A/m^2]
+ { Name J_vectors; NameOfPostProcessing Ele;
+ Operation {
+ Print[ Jv, OnElementsOf Vol_Ele, TimeLegend, File "Result_J_vectors.pos"];
+ }
+ }
+ // Magnitude of current density everywhere [A/m^2]
+ { Name J_magnitude; NameOfPostProcessing Ele;
+ Operation {
+ Print[ J, OnElementsOf Vol_Ele, TimeLegend, File "Result_J.pos"];
+ }
+ }
+ // Store the results in an ASCII file
+ { Name Cube_Top_Values_ASCII; NameOfPostProcessing Ele;
+ Operation {
+ Print[U, OnRegion Top1, File "Result_Cube1TopValues.txt", Format TimeTable];
+ Print[U, OnRegion Top2, File "Result_Cube2TopValues.txt", Format TimeTable];
+ Print[U, OnRegion Top3, File "Result_Cube3TopValues.txt", Format TimeTable];
+
+ Print[I, OnRegion Top1, File > "Result_Cube1TopValues.txt", Format TimeTable];
+ Print[I, OnRegion Top2, File > "Result_Cube2TopValues.txt", Format TimeTable];
+ Print[I, OnRegion Top3, File > "Result_Cube3TopValues.txt", Format TimeTable];
+ }
+ }
+
+}
diff --git a/CircuitCoupling/RLC_circuit_common.pro b/CircuitCoupling/RLC_circuit_common.pro
index 65360ad..cfa9d02 100644
--- a/CircuitCoupling/RLC_circuit_common.pro
+++ b/CircuitCoupling/RLC_circuit_common.pro
@@ -1,12 +1,12 @@
-// Physical numbers for volumes
-Cube1 = 1001;
-Cube2 = 1002;
-Cube3 = 1003;
-
-// Physical numbers for surfaces
-Cube1Top = 2001;
-Cube1Bottom = 2002;
-Cube2Top = 2003;
-Cube2Bottom = 2004;
-Cube3Top = 2005;
-Cube3Bottom = 2006;
+// Physical numbers for volumes
+Cube1 = 1001;
+Cube2 = 1002;
+Cube3 = 1003;
+
+// Physical numbers for surfaces
+Cube1Top = 2001;
+Cube1Bottom = 2002;
+Cube2Top = 2003;
+Cube2Bottom = 2004;
+Cube3Top = 2005;
+Cube3Bottom = 2006;
diff --git a/CircuitCoupling/R_circuit.geo b/CircuitCoupling/R_circuit.geo
index 77d9838..cc4e527 100644
--- a/CircuitCoupling/R_circuit.geo
+++ b/CircuitCoupling/R_circuit.geo
@@ -1,39 +1,39 @@
-// Just 4 cubes
-
-Include "R_circuit_common.pro";
-
-lc = 0.25; // Cjaracteristic length
-
-Point(1) = {0, 0, 0, lc};
-Extrude {1, 0, 0} {
- Point{1};
-}
-Extrude {0, 1, 0} {
- Line{1}; // Layers{10}; Recombine;
-}
-Extrude {0, 0, 1} {
- Surface{5}; // Layers{10}; Recombine;
-}
-Translate {2, 0, 0} {
- Duplicata { Volume{1}; }
-}
-Translate {0, 4, 0} {
- Duplicata { Volume{1}; }
-}
-Translate {2, 4, 0} {
- Duplicata { Volume{1}; }
-}
-
-Physical Surface(Cube1Top) = {27};
-Physical Surface(Cube1Bottom) = {5};
-Physical Surface(Cube2Top) = {34};
-Physical Surface(Cube2Bottom) = {29};
-Physical Surface(Cube3Top) = {61};
-Physical Surface(Cube3Bottom) = {56};
-Physical Surface(Cube4Top) = {88};
-Physical Surface(Cube4Bottom) = {83};
-
-Physical Volume(Cube1) = {1};
-Physical Volume(Cube2) = {28};
-Physical Volume(Cube3) = {55};
-Physical Volume(Cube4) = {82};
+// Just 4 cubes
+
+Include "R_circuit_common.pro";
+
+lc = 0.25; // Cjaracteristic length
+
+Point(1) = {0, 0, 0, lc};
+Extrude {1, 0, 0} {
+ Point{1};
+}
+Extrude {0, 1, 0} {
+ Line{1}; // Layers{10}; Recombine;
+}
+Extrude {0, 0, 1} {
+ Surface{5}; // Layers{10}; Recombine;
+}
+Translate {2, 0, 0} {
+ Duplicata { Volume{1}; }
+}
+Translate {0, 4, 0} {
+ Duplicata { Volume{1}; }
+}
+Translate {2, 4, 0} {
+ Duplicata { Volume{1}; }
+}
+
+Physical Surface(Cube1Top) = {27};
+Physical Surface(Cube1Bottom) = {5};
+Physical Surface(Cube2Top) = {34};
+Physical Surface(Cube2Bottom) = {29};
+Physical Surface(Cube3Top) = {61};
+Physical Surface(Cube3Bottom) = {56};
+Physical Surface(Cube4Top) = {88};
+Physical Surface(Cube4Bottom) = {83};
+
+Physical Volume(Cube1) = {1};
+Physical Volume(Cube2) = {28};
+Physical Volume(Cube3) = {55};
+Physical Volume(Cube4) = {82};
diff --git a/CircuitCoupling/R_circuit.pro b/CircuitCoupling/R_circuit.pro
index 8ec804b..0fabf0e 100644
--- a/CircuitCoupling/R_circuit.pro
+++ b/CircuitCoupling/R_circuit.pro
@@ -1,342 +1,342 @@
-/* -------------------------------------------------------------------
- Tutorial 8a : circuit coupling - resistive circuit
-
- Features:
- - Electrokinetic formulation coupled with resistive circuit
- - Definition of circuit elements (sources, resistances)
- - Implementation of a netlist
-
- To compute the solution in a terminal:
- getdp R_circuit -solve static -pos Cube_Top_Values_ASCII
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > R_circuit.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-/*
- This example shows how to implement a circuit with discrete elements in a
- finite element simulation. Only lumped resistors, voltage- and current-sources
- are used. There are four separate cubes, each with a certain conductivity. The
- bottom of all cubes is kept at a constant voltage via the constraint
- Voltage_3D. The top of the cubes are connected with a circuit according the
- `R_circuit.jpg' schematic.
-*/
-
-Include "R_circuit_common.pro";
-
-// FEM domain group data
-Group {
- // Surfaces
- Top1 = Region[Cube1Top];
- Bottom1 = Region[Cube1Bottom];
- Top2 = Region[Cube2Top];
- Bottom2 = Region[Cube2Bottom];
- Top3 = Region[Cube3Top];
- Bottom3 = Region[Cube3Bottom];
- Top4 = Region[Cube4Top];
- Bottom4 = Region[Cube4Bottom];
-
- // Volumes
- Cube1 = Region[Cube1];
- Cube2 = Region[Cube2];
- Cube3 = Region[Cube3];
- Cube4 = Region[Cube4];
-
- // FEM Electrical regions
- // * all volumes:
- Vol_Ele = Region[{Cube1, Cube2, Cube3, Cube4}];
- // * all surfaces connected to the lumped element circuit
- Sur_Ele = Region[{Top1, Bottom1, Top2, Bottom2, Top3, Bottom3, Top4, Bottom4}];
- // * total electrical computation domain:
- VolWithSur_Ele = Region[{Vol_Ele, Sur_Ele}];
-}
-
-// Circuit group data (fictive regions for the circuit elements)
-Group {
- // Sources
- CurrentSource1 = Region[{3001}];
- VoltageSource1 = Region[{3002}];
-
- SourceI_Cir = Region[{CurrentSource1}]; // all current sources
- SourceV_Cir = Region[{VoltageSource1}]; // all voltage sources
- Sources_Cir = Region[{SourceI_Cir, SourceV_Cir}];
-
- // Resistors
- Res1 = Region[{4001}];
- Res2 = Region[{4002}];
- Res3 = Region[{4003}];
- Res4 = Region[{4004}];
-
- Resistance_Cir = Region[{Res1, Res2, Res3, Res4}]; // All resistors
-
- // Complete circuit domain containing all circuit elements
- Domain_Cir = Region[{Resistance_Cir, SourceI_Cir, SourceV_Cir}];
-}
-
-// FEM domain function data
-Function {
- // Absolute voltage at the bottom of all cubes; set via constraint Voltage_3D,
- // not via a voltage source
- Vbottom = 4.0;
-
- // Geometry of a cube
- w = 1.0; // Width [m]
- l = 1.0; // Length [m]
- h = 1.0; // Height [m]
-
- // Resistance
- Rcube1 = 20.0; // Resistance of cube 1 [Ohm]
- Rcube2 = 40.0; // Resistance of cube 2 [Ohm]
- Rcube3 = 60.0; // Resistance of cube 3 [Ohm]
- Rcube4 = 10.0; // Resistance of cube 4 [Ohm]
-
- // Specific electrical conductivity [S*m/m^2]
- kappa[Cube1] = h / (w * l * Rcube1);
- kappa[Cube2] = h / (w * l * Rcube2);
- kappa[Cube3] = h / (w * l * Rcube3);
- kappa[Cube4] = h / (w * l * Rcube4);
-}
-
-// Circuit domain function data
-Function {
- // External impedances functions
- R[Res1] = 10.0;
- R[Res2] = 20.0;
- R[Res3] = 15.0;
- R[Res4] = 10.0;
-}
-
-// FEM domain constraint data
-Constraint {
- { Name Current_3D ; Type Assign ;
- Case {
- }
- }
- { Name Voltage_3D ; Type Assign ;
- Case {
- { Region Bottom1; Type Assign; Value Vbottom; }
- { Region Bottom2; Type Assign; Value Vbottom; }
- { Region Bottom3; Type Assign; Value Vbottom; }
- { Region Bottom4; Type Assign; Value Vbottom; }
- }
- }
-}
-
-// Circuit domain constraint data
-Constraint {
- { Name Current_Cir ;
- Case {
- { Region CurrentSource1; Value 1.0; } // CurrentSource1 has 1.0 A
- }
- }
- { Name Voltage_Cir ;
- Case {
- { Region VoltageSource1; Value 10.0; } // VoltageSource1 has 10.0 V
- }
- }
- { Name ElectricalCircuit ; Type Network ;
- Case Circuit1 {
- // Here the circuit netlist is implemented. The important thing is that
- // each surface of the 3D geometry which is connected to the circuit
- // (Sur_Ele) has a single voltage and current, but in the netlist they
- // appear with two terminals (two nodes). The voltage between the two
- // nodes corresponds to the absolute voltage of the surface. The current
- // through the two nodes is the current flowing through the surface. In
- // this simple case here we need the voltage drop across a cube (e.g. cube
- // 1) in the netlist rather than the absolute voltage. Therefore the
- // bottom-voltage has to be subtracted from the top-voltage. This is
- // accomplished by connecting both surfaces anti-serial (e.g. at node 4;
- // The voltage drop across cube 1 is then between node 2 and node 10).
-
- { Region VoltageSource1; Branch{1, 10}; }
- { Region Res1; Branch{1, 2}; }
- // Voltage between node 2 and node 4 corresponds to the absolute voltage
- // of Top1:
- { Region Top1; Branch{2, 4}; }
- // Note the reverse order of the nodes here - it's for subtracting the
- // bottom voltage:
- { Region Bottom1; Branch{10, 4}; }
- // Voltage between node 3 and node 5 corresponds to the absolute voltage
- // of Top2:
- { Region Res2; Branch{2, 3}; }
- { Region Top2; Branch{3, 5}; }
- // Note the reverse order of the nodes here! It's for subtracting the
- // bottom voltage.:
- { Region Bottom2; Branch{10, 5}; }
-
- { Region CurrentSource1; Branch{6, 10}; }
- { Region Res3; Branch{6, 10}; }
- // Voltage between node 6 and node 8 corresponds to the absolute voltage
- // of Top3:
- { Region Top3; Branch{6, 8}; }
- // Note the reverse order of the nodes here! It's for subtracting the
- // bottom voltage.:
- { Region Bottom3; Branch{10, 8}; }
- { Region Res4; Branch{6, 7}; }
- // Voltage between node 7 and node 9 corresponds to the absolute voltage
- // of Top4:
- { Region Top4; Branch{7, 9}; }
- // Note the reverse order of the nodes here! It's for subtracting the
- // bottom voltage:
- { Region Bottom4; Branch{10, 9}; }
- }
- }
-}
-
-Jacobian {
- { Name JVol ;
- Case {
- { Region Region[{Vol_Ele}]; Jacobian Vol; }
- { Region Region[{Sur_Ele}]; Jacobian Sur; }
- }
- }
-}
-
-Integration {
- { Name I1 ;
- Case {
- { Type Gauss ;
- Case {
- { GeoElement Point ; NumberOfPoints 1 ; }
- { GeoElement Line ; NumberOfPoints 5 ; }
- { GeoElement Triangle ; NumberOfPoints 6 ; }
- { GeoElement Quadrangle ; NumberOfPoints 7 ; }
- { GeoElement Tetrahedron ; NumberOfPoints 15 ; }
- { GeoElement Hexahedron ; NumberOfPoints 34 ; }
- { GeoElement Prism ; NumberOfPoints 21 ; }
- }
- }
- }
- }
-}
-
-
-FunctionSpace {
- { Name Hgrad_V; Type Form0;
- BasisFunction {
- // All nodes but the grouped nodes of the surfaces for connecting the
- // circuitry
- { Name sn; NameOfCoef vn; Function BF_Node;
- Support VolWithSur_Ele; Entity NodesOf[ All, Not Sur_Ele ]; }
- // Grouped nodes: Each surface of Sur_Ele has just one single voltage ->
- // each surface is just one node effectively
- { Name sf; NameOfCoef vf; Function BF_GroupOfNodes;
- Support VolWithSur_Ele; Entity GroupsOfNodesOf[ Sur_Ele ]; }
- }
- GlobalQuantity {
- // Voltage of the surfaces of Sur_Ele
- { Name U; Type AliasOf; NameOfCoef vf; }
- // Current flowing through the surfaces
- { Name I; Type AssociatedWith; NameOfCoef vf; }
- }
- Constraint {
- { NameOfCoef vn; EntityType NodesOf ; NameOfConstraint Voltage_3D; }
- { NameOfCoef U; EntityType GroupsOfNodesOf ; NameOfConstraint Voltage_3D; }
- { NameOfCoef I; EntityType GroupsOfNodesOf ; NameOfConstraint Current_3D; }
- }
- }
-
- { Name Hregion_Cir; Type Scalar;
- BasisFunction {
- { Name sn; NameOfCoef ir; Function BF_Region;
- Support Domain_Cir; Entity Domain_Cir; }
- }
- GlobalQuantity {
- { Name Iz; Type AliasOf; NameOfCoef ir; }
- { Name Uz; Type AssociatedWith; NameOfCoef ir; }
- }
- Constraint {
- { NameOfCoef Uz ; EntityType Region ; NameOfConstraint Voltage_Cir ; }
- { NameOfCoef Iz ; EntityType Region ; NameOfConstraint Current_Cir ; }
- }
- }
-}
-
-Formulation {
- { Name static; Type FemEquation;
- Quantity {
- { Name V; Type Local; NameOfSpace Hgrad_V; }
- { Name U; Type Global; NameOfSpace Hgrad_V [U]; }
- { Name I; Type Global; NameOfSpace Hgrad_V [I]; }
- { Name Uz; Type Global; NameOfSpace Hregion_Cir [Uz]; }
- { Name Iz; Type Global; NameOfSpace Hregion_Cir [Iz]; }
- }
- Equation {
- // FEM domain
- Galerkin { [ kappa[] * Dof{d V}, {d V} ];
- In Vol_Ele; Integration I1; Jacobian JVol; }
- GlobalTerm { [ Dof{I} , {U} ]; In Sur_Ele; }
-
- // Circuit related terms: Resistance equation
- GlobalTerm { [ Dof{Uz}, {Iz} ]; In Resistance_Cir; }
- GlobalTerm { [ R[] * Dof{Iz}, {Iz} ]; In Resistance_Cir; }
-
- // Here is the connection between the circuit and the finite element simulation
- GlobalEquation { Type Network; NameOfConstraint ElectricalCircuit;
- { Node {I}; Loop {U}; Equation {I}; In Sur_Ele; }
- { Node {Iz}; Loop {Uz}; Equation {Uz}; In Domain_Cir; }
- }
- }
- }
-}
-
-Resolution {
- { Name static;
- System {
- { Name A; NameOfFormulation static; }
- }
- Operation {
- Generate[A];
- Solve[A];
- SaveSolution[A];
- }
- }
-}
-
-PostProcessing {
- { Name Ele; NameOfFormulation static;
- Quantity {
- { Name V; Value{ Local{ [ {V} ]; In Vol_Ele; Jacobian JVol;} } }
- { Name Jv; Value{ Local{ [ -kappa[]*{d V} ]; In Vol_Ele; Jacobian JVol;} } }
- { Name J; Value{ Local{ [ Norm[kappa[]*{d V}] ]; In Vol_Ele; Jacobian JVol;} } }
- { Name U; Value { Term { [ {U} ]; In Sur_Ele; } } }
- { Name I; Value { Term { [ {I} ]; In Sur_Ele; } } }
- }
- }
-}
-
-PostOperation {
- // Absolute voltage [V]
- { Name V; NameOfPostProcessing Ele;
- Operation {
- Print[ V, OnElementsOf Vol_Ele, File "Result_V.pos"];
- }
- }
- // Current density vectors [A/m^2]
- { Name J_vectors; NameOfPostProcessing Ele;
- Operation {
- Print[ Jv, OnElementsOf Vol_Ele, File "Result_J_vectors.pos"];
- }
- }
- // Magnitude of current density [A/m^2]
- { Name J_magnitude; NameOfPostProcessing Ele;
- Operation {
- Print[ J, OnElementsOf Vol_Ele, File "Result_J.pos"];
- }
- }
- // Store the results in an ASCII file
- { Name Cube_Top_Values_ASCII; NameOfPostProcessing Ele;
- Operation {
- Print[U, OnRegion Top1, File "Result_CubeTopValues.txt", Format SimpleTable];
- Print[U, OnRegion Top2, File > "Result_CubeTopValues.txt", Format SimpleTable];
- Print[U, OnRegion Top3, File > "Result_CubeTopValues.txt", Format SimpleTable];
- Print[U, OnRegion Top4, File > "Result_CubeTopValues.txt", Format SimpleTable];
-
- Print[I, OnRegion Top1, File > "Result_CubeTopValues.txt", Format SimpleTable];
- Print[I, OnRegion Top2, File > "Result_CubeTopValues.txt", Format SimpleTable];
- Print[I, OnRegion Top3, File > "Result_CubeTopValues.txt", Format SimpleTable];
- Print[I, OnRegion Top4, File > "Result_CubeTopValues.txt", Format SimpleTable];
- }
- }
-}
+/* -------------------------------------------------------------------
+ Tutorial 8a : circuit coupling - resistive circuit
+
+ Features:
+ - Electrokinetic formulation coupled with resistive circuit
+ - Definition of circuit elements (sources, resistances)
+ - Implementation of a netlist
+
+ To compute the solution in a terminal:
+ getdp R_circuit -solve static -pos Cube_Top_Values_ASCII
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > R_circuit.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+/*
+ This example shows how to implement a circuit with discrete elements in a
+ finite element simulation. Only lumped resistors, voltage- and current-sources
+ are used. There are four separate cubes, each with a certain conductivity. The
+ bottom of all cubes is kept at a constant voltage via the constraint
+ Voltage_3D. The top of the cubes are connected with a circuit according the
+ `R_circuit.jpg' schematic.
+*/
+
+Include "R_circuit_common.pro";
+
+// FEM domain group data
+Group {
+ // Surfaces
+ Top1 = Region[Cube1Top];
+ Bottom1 = Region[Cube1Bottom];
+ Top2 = Region[Cube2Top];
+ Bottom2 = Region[Cube2Bottom];
+ Top3 = Region[Cube3Top];
+ Bottom3 = Region[Cube3Bottom];
+ Top4 = Region[Cube4Top];
+ Bottom4 = Region[Cube4Bottom];
+
+ // Volumes
+ Cube1 = Region[Cube1];
+ Cube2 = Region[Cube2];
+ Cube3 = Region[Cube3];
+ Cube4 = Region[Cube4];
+
+ // FEM Electrical regions
+ // * all volumes:
+ Vol_Ele = Region[{Cube1, Cube2, Cube3, Cube4}];
+ // * all surfaces connected to the lumped element circuit
+ Sur_Ele = Region[{Top1, Bottom1, Top2, Bottom2, Top3, Bottom3, Top4, Bottom4}];
+ // * total electrical computation domain:
+ VolWithSur_Ele = Region[{Vol_Ele, Sur_Ele}];
+}
+
+// Circuit group data (fictive regions for the circuit elements)
+Group {
+ // Sources
+ CurrentSource1 = Region[{3001}];
+ VoltageSource1 = Region[{3002}];
+
+ SourceI_Cir = Region[{CurrentSource1}]; // all current sources
+ SourceV_Cir = Region[{VoltageSource1}]; // all voltage sources
+ Sources_Cir = Region[{SourceI_Cir, SourceV_Cir}];
+
+ // Resistors
+ Res1 = Region[{4001}];
+ Res2 = Region[{4002}];
+ Res3 = Region[{4003}];
+ Res4 = Region[{4004}];
+
+ Resistance_Cir = Region[{Res1, Res2, Res3, Res4}]; // All resistors
+
+ // Complete circuit domain containing all circuit elements
+ Domain_Cir = Region[{Resistance_Cir, SourceI_Cir, SourceV_Cir}];
+}
+
+// FEM domain function data
+Function {
+ // Absolute voltage at the bottom of all cubes; set via constraint Voltage_3D,
+ // not via a voltage source
+ Vbottom = 4.0;
+
+ // Geometry of a cube
+ w = 1.0; // Width [m]
+ l = 1.0; // Length [m]
+ h = 1.0; // Height [m]
+
+ // Resistance
+ Rcube1 = 20.0; // Resistance of cube 1 [Ohm]
+ Rcube2 = 40.0; // Resistance of cube 2 [Ohm]
+ Rcube3 = 60.0; // Resistance of cube 3 [Ohm]
+ Rcube4 = 10.0; // Resistance of cube 4 [Ohm]
+
+ // Specific electrical conductivity [S*m/m^2]
+ kappa[Cube1] = h / (w * l * Rcube1);
+ kappa[Cube2] = h / (w * l * Rcube2);
+ kappa[Cube3] = h / (w * l * Rcube3);
+ kappa[Cube4] = h / (w * l * Rcube4);
+}
+
+// Circuit domain function data
+Function {
+ // External impedances functions
+ R[Res1] = 10.0;
+ R[Res2] = 20.0;
+ R[Res3] = 15.0;
+ R[Res4] = 10.0;
+}
+
+// FEM domain constraint data
+Constraint {
+ { Name Current_3D ; Type Assign ;
+ Case {
+ }
+ }
+ { Name Voltage_3D ; Type Assign ;
+ Case {
+ { Region Bottom1; Type Assign; Value Vbottom; }
+ { Region Bottom2; Type Assign; Value Vbottom; }
+ { Region Bottom3; Type Assign; Value Vbottom; }
+ { Region Bottom4; Type Assign; Value Vbottom; }
+ }
+ }
+}
+
+// Circuit domain constraint data
+Constraint {
+ { Name Current_Cir ;
+ Case {
+ { Region CurrentSource1; Value 1.0; } // CurrentSource1 has 1.0 A
+ }
+ }
+ { Name Voltage_Cir ;
+ Case {
+ { Region VoltageSource1; Value 10.0; } // VoltageSource1 has 10.0 V
+ }
+ }
+ { Name ElectricalCircuit ; Type Network ;
+ Case Circuit1 {
+ // Here the circuit netlist is implemented. The important thing is that
+ // each surface of the 3D geometry which is connected to the circuit
+ // (Sur_Ele) has a single voltage and current, but in the netlist they
+ // appear with two terminals (two nodes). The voltage between the two
+ // nodes corresponds to the absolute voltage of the surface. The current
+ // through the two nodes is the current flowing through the surface. In
+ // this simple case here we need the voltage drop across a cube (e.g. cube
+ // 1) in the netlist rather than the absolute voltage. Therefore the
+ // bottom-voltage has to be subtracted from the top-voltage. This is
+ // accomplished by connecting both surfaces anti-serial (e.g. at node 4;
+ // The voltage drop across cube 1 is then between node 2 and node 10).
+
+ { Region VoltageSource1; Branch{1, 10}; }
+ { Region Res1; Branch{1, 2}; }
+ // Voltage between node 2 and node 4 corresponds to the absolute voltage
+ // of Top1:
+ { Region Top1; Branch{2, 4}; }
+ // Note the reverse order of the nodes here - it's for subtracting the
+ // bottom voltage:
+ { Region Bottom1; Branch{10, 4}; }
+ // Voltage between node 3 and node 5 corresponds to the absolute voltage
+ // of Top2:
+ { Region Res2; Branch{2, 3}; }
+ { Region Top2; Branch{3, 5}; }
+ // Note the reverse order of the nodes here! It's for subtracting the
+ // bottom voltage.:
+ { Region Bottom2; Branch{10, 5}; }
+
+ { Region CurrentSource1; Branch{6, 10}; }
+ { Region Res3; Branch{6, 10}; }
+ // Voltage between node 6 and node 8 corresponds to the absolute voltage
+ // of Top3:
+ { Region Top3; Branch{6, 8}; }
+ // Note the reverse order of the nodes here! It's for subtracting the
+ // bottom voltage.:
+ { Region Bottom3; Branch{10, 8}; }
+ { Region Res4; Branch{6, 7}; }
+ // Voltage between node 7 and node 9 corresponds to the absolute voltage
+ // of Top4:
+ { Region Top4; Branch{7, 9}; }
+ // Note the reverse order of the nodes here! It's for subtracting the
+ // bottom voltage:
+ { Region Bottom4; Branch{10, 9}; }
+ }
+ }
+}
+
+Jacobian {
+ { Name JVol ;
+ Case {
+ { Region Region[{Vol_Ele}]; Jacobian Vol; }
+ { Region Region[{Sur_Ele}]; Jacobian Sur; }
+ }
+ }
+}
+
+Integration {
+ { Name I1 ;
+ Case {
+ { Type Gauss ;
+ Case {
+ { GeoElement Point ; NumberOfPoints 1 ; }
+ { GeoElement Line ; NumberOfPoints 5 ; }
+ { GeoElement Triangle ; NumberOfPoints 6 ; }
+ { GeoElement Quadrangle ; NumberOfPoints 7 ; }
+ { GeoElement Tetrahedron ; NumberOfPoints 15 ; }
+ { GeoElement Hexahedron ; NumberOfPoints 34 ; }
+ { GeoElement Prism ; NumberOfPoints 21 ; }
+ }
+ }
+ }
+ }
+}
+
+
+FunctionSpace {
+ { Name Hgrad_V; Type Form0;
+ BasisFunction {
+ // All nodes but the grouped nodes of the surfaces for connecting the
+ // circuitry
+ { Name sn; NameOfCoef vn; Function BF_Node;
+ Support VolWithSur_Ele; Entity NodesOf[ All, Not Sur_Ele ]; }
+ // Grouped nodes: Each surface of Sur_Ele has just one single voltage ->
+ // each surface is just one node effectively
+ { Name sf; NameOfCoef vf; Function BF_GroupOfNodes;
+ Support VolWithSur_Ele; Entity GroupsOfNodesOf[ Sur_Ele ]; }
+ }
+ GlobalQuantity {
+ // Voltage of the surfaces of Sur_Ele
+ { Name U; Type AliasOf; NameOfCoef vf; }
+ // Current flowing through the surfaces
+ { Name I; Type AssociatedWith; NameOfCoef vf; }
+ }
+ Constraint {
+ { NameOfCoef vn; EntityType NodesOf ; NameOfConstraint Voltage_3D; }
+ { NameOfCoef U; EntityType GroupsOfNodesOf ; NameOfConstraint Voltage_3D; }
+ { NameOfCoef I; EntityType GroupsOfNodesOf ; NameOfConstraint Current_3D; }
+ }
+ }
+
+ { Name Hregion_Cir; Type Scalar;
+ BasisFunction {
+ { Name sn; NameOfCoef ir; Function BF_Region;
+ Support Domain_Cir; Entity Domain_Cir; }
+ }
+ GlobalQuantity {
+ { Name Iz; Type AliasOf; NameOfCoef ir; }
+ { Name Uz; Type AssociatedWith; NameOfCoef ir; }
+ }
+ Constraint {
+ { NameOfCoef Uz ; EntityType Region ; NameOfConstraint Voltage_Cir ; }
+ { NameOfCoef Iz ; EntityType Region ; NameOfConstraint Current_Cir ; }
+ }
+ }
+}
+
+Formulation {
+ { Name static; Type FemEquation;
+ Quantity {
+ { Name V; Type Local; NameOfSpace Hgrad_V; }
+ { Name U; Type Global; NameOfSpace Hgrad_V [U]; }
+ { Name I; Type Global; NameOfSpace Hgrad_V [I]; }
+ { Name Uz; Type Global; NameOfSpace Hregion_Cir [Uz]; }
+ { Name Iz; Type Global; NameOfSpace Hregion_Cir [Iz]; }
+ }
+ Equation {
+ // FEM domain
+ Integral { [ kappa[] * Dof{d V}, {d V} ];
+ In Vol_Ele; Integration I1; Jacobian JVol; }
+ GlobalTerm { [ Dof{I} , {U} ]; In Sur_Ele; }
+
+ // Circuit related terms: Resistance equation
+ GlobalTerm { [ Dof{Uz}, {Iz} ]; In Resistance_Cir; }
+ GlobalTerm { [ R[] * Dof{Iz}, {Iz} ]; In Resistance_Cir; }
+
+ // Here is the connection between the circuit and the finite element simulation
+ GlobalEquation { Type Network; NameOfConstraint ElectricalCircuit;
+ { Node {I}; Loop {U}; Equation {I}; In Sur_Ele; }
+ { Node {Iz}; Loop {Uz}; Equation {Uz}; In Domain_Cir; }
+ }
+ }
+ }
+}
+
+Resolution {
+ { Name static;
+ System {
+ { Name A; NameOfFormulation static; }
+ }
+ Operation {
+ Generate[A];
+ Solve[A];
+ SaveSolution[A];
+ }
+ }
+}
+
+PostProcessing {
+ { Name Ele; NameOfFormulation static;
+ Quantity {
+ { Name V; Value{ Local{ [ {V} ]; In Vol_Ele; Jacobian JVol;} } }
+ { Name Jv; Value{ Local{ [ -kappa[]*{d V} ]; In Vol_Ele; Jacobian JVol;} } }
+ { Name J; Value{ Local{ [ Norm[kappa[]*{d V}] ]; In Vol_Ele; Jacobian JVol;} } }
+ { Name U; Value { Term { [ {U} ]; In Sur_Ele; } } }
+ { Name I; Value { Term { [ {I} ]; In Sur_Ele; } } }
+ }
+ }
+}
+
+PostOperation {
+ // Absolute voltage [V]
+ { Name V; NameOfPostProcessing Ele;
+ Operation {
+ Print[ V, OnElementsOf Vol_Ele, File "Result_V.pos"];
+ }
+ }
+ // Current density vectors [A/m^2]
+ { Name J_vectors; NameOfPostProcessing Ele;
+ Operation {
+ Print[ Jv, OnElementsOf Vol_Ele, File "Result_J_vectors.pos"];
+ }
+ }
+ // Magnitude of current density [A/m^2]
+ { Name J_magnitude; NameOfPostProcessing Ele;
+ Operation {
+ Print[ J, OnElementsOf Vol_Ele, File "Result_J.pos"];
+ }
+ }
+ // Store the results in an ASCII file
+ { Name Cube_Top_Values_ASCII; NameOfPostProcessing Ele;
+ Operation {
+ Print[U, OnRegion Top1, File "Result_CubeTopValues.txt", Format SimpleTable];
+ Print[U, OnRegion Top2, File > "Result_CubeTopValues.txt", Format SimpleTable];
+ Print[U, OnRegion Top3, File > "Result_CubeTopValues.txt", Format SimpleTable];
+ Print[U, OnRegion Top4, File > "Result_CubeTopValues.txt", Format SimpleTable];
+
+ Print[I, OnRegion Top1, File > "Result_CubeTopValues.txt", Format SimpleTable];
+ Print[I, OnRegion Top2, File > "Result_CubeTopValues.txt", Format SimpleTable];
+ Print[I, OnRegion Top3, File > "Result_CubeTopValues.txt", Format SimpleTable];
+ Print[I, OnRegion Top4, File > "Result_CubeTopValues.txt", Format SimpleTable];
+ }
+ }
+}
diff --git a/CircuitCoupling/R_circuit_common.pro b/CircuitCoupling/R_circuit_common.pro
index 3384474..80415a6 100644
--- a/CircuitCoupling/R_circuit_common.pro
+++ b/CircuitCoupling/R_circuit_common.pro
@@ -1,15 +1,15 @@
-// Physical numbers for volumes
-Cube1 = 1001;
-Cube2 = 1002;
-Cube3 = 1003;
-Cube4 = 1004;
-
-// Physical numbers for surfaces
-Cube1Top = 2001;
-Cube1Bottom = 2002;
-Cube2Top = 2003;
-Cube2Bottom = 2004;
-Cube3Top = 2005;
-Cube3Bottom = 2006;
-Cube4Top = 2007;
-Cube4Bottom = 2008;
+// Physical numbers for volumes
+Cube1 = 1001;
+Cube2 = 1002;
+Cube3 = 1003;
+Cube4 = 1004;
+
+// Physical numbers for surfaces
+Cube1Top = 2001;
+Cube1Bottom = 2002;
+Cube2Top = 2003;
+Cube2Bottom = 2004;
+Cube3Top = 2005;
+Cube3Bottom = 2006;
+Cube4Top = 2007;
+Cube4Bottom = 2008;
diff --git a/Elasticity/wrench2D.geo b/Elasticity/wrench2D.geo
index 782b701..d107af1 100644
--- a/Elasticity/wrench2D.geo
+++ b/Elasticity/wrench2D.geo
@@ -1,72 +1,72 @@
-
-Include "wrench2D_common.pro";
-
-Solver.AutoMesh = 2;
-
-lc = Refine;
-lc2 = lc; // nut region
-lc3 = lc/5; // edge grip region
-
-Ri = 0.494*in;
-Re = 0.8*in;
-L = LLength;
-LL = 1*in;
-E = 0.625*in;
-F = Width;
-D = 0.45*in; // Nut
-
-theta = Inclination;
-
-Point(1) = { 0, 0, 0, lc2};
-Point(2) = { -Ri, 0, 0, lc2};
-th1 = Asin[E/2./Ri];
-Point(3) = { -Ri + Ri*Cos[th1], Ri*Sin[th1], 0, lc2};
-th2 = Asin[E/2./Re];
-Point(4) = { -Re*Cos[th2]+D, Re*Sin[th2], 0, lc3};
-Point(5) = { -Re*Cos[th2], Re*Sin[th2], 0, lc2};
-th3 = th2 - theta;
-Point(6) = { Re*Cos[th3], Re*Sin[th3], 0, lc};
-Point(7) = { (L-LL)*Cos[theta]+F/2.*Sin[theta],
- -(L-LL)*Sin[theta]+F/2.*Cos[theta], 0, lc};
-Point(8) = { L*Cos[theta]+F/2.*Sin[theta],
- -L*Sin[theta]+F/2.*Cos[theta], 0, lc};
-Point(9) = { L*Cos[theta]-F/2.*Sin[theta],
- -L*Sin[theta]-F/2.*Cos[theta], 0, lc};
-th4 = -th2 - theta;
-Point(10) = { Re*Cos[th4], Re*Sin[th4], 0, lc};
-Point(11) = { -Re*Cos[th2], -Re*Sin[th2], 0, lc2};
-Point(12) = { -Re*Cos[th2]+D, -Re*Sin[th2], 0, lc3};
-Point(13) = { -Ri + Ri*Cos[th1], -Ri*Sin[th1], 0, lc2};
-
-contour[] = {};
-contour[] += newl; Circle(newl) = {1,2,3};
-contour[] += newl; Line(newl) = {3,4};
-contour[] += newl; cl1=newl; Line(newl) = {4,5};
-contour[] += newl; Circle(newl) = {5,1,6};
-contour[] += newl; Line(newl) = {6,7};
-contour[] += newl; cl2=newl; Line(newl) = {7,8};
-contour[] += newl; Line(newl) = {8,9};
-contour[] += newl; Line(newl) = {9,10};
-contour[] += newl; Circle(newl) = {10,1,11};
-contour[] += newl; cl3=newl; Line(newl) = {11,12};
-contour[] += newl; Line(newl) = {12,13};
-contour[] += newl; Circle(newl) = {13,2,1};
-ll=newll; Line Loop(ll) = { contour[] };
-
-wrench=news; Plane Surface(wrench) = {-ll};
-
-/* Using quadrangular elements instead of triangular elements is pretty simple.
- You just have to invoke the Recombine command at this place.
- GetDP deals will all the rest by itself.
- */
-If(Recomb==1)
- Recombine Surface{wrench};
-EndIf
-
-Physical Surface(1)= wrench;
-Physical Line(2)= {cl1, cl3};
-Physical Line(3)= {cl2};
-
-
-
-
+
+Include "wrench2D_common.pro";
+
+Solver.AutoMesh = 2;
+
+lc = Refine;
+lc2 = lc; // nut region
+lc3 = lc/5; // edge grip region
+
+Ri = 0.494*in;
+Re = 0.8*in;
+L = LLength;
+LL = 1*in;
+E = 0.625*in;
+F = Width;
+D = 0.45*in; // Nut
+
+theta = Inclination;
+
+Point(1) = { 0, 0, 0, lc2};
+Point(2) = { -Ri, 0, 0, lc2};
+th1 = Asin[E/2./Ri];
+Point(3) = { -Ri + Ri*Cos[th1], Ri*Sin[th1], 0, lc2};
+th2 = Asin[E/2./Re];
+Point(4) = { -Re*Cos[th2]+D, Re*Sin[th2], 0, lc3};
+Point(5) = { -Re*Cos[th2], Re*Sin[th2], 0, lc2};
+th3 = th2 - theta;
+Point(6) = { Re*Cos[th3], Re*Sin[th3], 0, lc};
+Point(7) = { (L-LL)*Cos[theta]+F/2.*Sin[theta],
+ -(L-LL)*Sin[theta]+F/2.*Cos[theta], 0, lc};
+Point(8) = { L*Cos[theta]+F/2.*Sin[theta],
+ -L*Sin[theta]+F/2.*Cos[theta], 0, lc};
+Point(9) = { L*Cos[theta]-F/2.*Sin[theta],
+ -L*Sin[theta]-F/2.*Cos[theta], 0, lc};
+th4 = -th2 - theta;
+Point(10) = { Re*Cos[th4], Re*Sin[th4], 0, lc};
+Point(11) = { -Re*Cos[th2], -Re*Sin[th2], 0, lc2};
+Point(12) = { -Re*Cos[th2]+D, -Re*Sin[th2], 0, lc3};
+Point(13) = { -Ri + Ri*Cos[th1], -Ri*Sin[th1], 0, lc2};
+
+contour[] = {};
+contour[] += newl; Circle(newl) = {1,2,3};
+contour[] += newl; Line(newl) = {3,4};
+contour[] += newl; cl1=newl; Line(newl) = {4,5};
+contour[] += newl; Circle(newl) = {5,1,6};
+contour[] += newl; Line(newl) = {6,7};
+contour[] += newl; cl2=newl; Line(newl) = {7,8};
+contour[] += newl; Line(newl) = {8,9};
+contour[] += newl; Line(newl) = {9,10};
+contour[] += newl; Circle(newl) = {10,1,11};
+contour[] += newl; cl3=newl; Line(newl) = {11,12};
+contour[] += newl; Line(newl) = {12,13};
+contour[] += newl; Circle(newl) = {13,2,1};
+ll=newll; Line Loop(ll) = { contour[] };
+
+wrench=news; Plane Surface(wrench) = {-ll};
+
+/* Using quadrangular elements instead of triangular elements is pretty simple.
+ You just have to invoke the Recombine command at this place.
+ GetDP deals will all the rest by itself.
+ */
+If(Recomb==1)
+ Recombine Surface{wrench};
+EndIf
+
+Physical Surface(1)= wrench;
+Physical Line(2)= {cl1, cl3};
+Physical Line(3)= {cl2};
+
+
+
+
diff --git a/Elasticity/wrench2D.pro b/Elasticity/wrench2D.pro
index fab3a7f..ce97783 100644
--- a/Elasticity/wrench2D.pro
+++ b/Elasticity/wrench2D.pro
@@ -1,366 +1,365 @@
-/* -------------------------------------------------------------------
- Tutorial 3 : linear elastic model of a wrench
-
- Features:
- - "Grad u" GetDP specific formulation for linear elasticity
- - first and second order elements
- - triangular and quadrangular elements
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > wrench.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-/* Linear elasticity with GetDP:
-
- GetDP has a peculiar way to deal with linear elasticity.
- Instead of vector field "u = Vector[ ux, uy, uz ]",
- the displacement field is regarded as two (2D case) or 3 (3D case) scalar fields.
- Unlike conventional formulations, GetDP's formulation is written
- in terms of the gradient "Grad u" of the displacement field,
- which is a non-symmetric tensor, and the needed symmetrization
- (to define the strain tensor and relate it to the stress tensor)
- is done through the constitutive relationship (Hooke law).
- The reason for this unusual formulation is to be able to use also for elastic problems
- the powerful geometrical and homological kernel of GetDP,
- which relies on the operators Grad, Curl and Div.
-
- The "Grad u" formulation entails a small increase of assembly work
- but makes in counterpart lots of geometrical features
- implemented in GetDP (change of coordinates, function spaces, etc...)
- applicable to elastic problems out-of-the-box,
- since the scalar fields { ux, uy, uz } have exactly the same geometrical properties
- as, e.g. a scalar electrip potential or a temperature field.
-*/
-
-
-Include "wrench2D_common.pro";
-
-Young = 1e9 *
- DefineNumber[ 200, Name "Material/Young modulus [GPa]"];
-Poisson =
- DefineNumber[ 0.3, Name "Material/Poisson coefficient []"];
-AppliedForce =
- DefineNumber[ 100, Name "Material/Applied force [N]"];
-
-// Approximation of the maximum deflection by an analytical model:
-// Deflection = PL^3/(3EI) with I = Width^3*Thickness/12
-Deflection =
- DefineNumber[4*AppliedForce*((LLength-0.018)/Width)^3/(Young*Thickness)*1e3,
- Name "Solution/Deflection (analytical) [mm]", ReadOnly 1];
-
-Group {
- // Physical regions: Give explicit labels to the regions defined in the .geo file
- Wrench = Region[ 1 ];
- Grip = Region[ 2 ];
- Force = Region[ 3 ];
-
- // Abstract regions:
- Vol_Elast_Mec = Region[ { Wrench } ];
- Vol_Force_Mec = Region[ { Wrench } ];
- Sur_Clamp_Mec = Region[ { Grip } ];
- Sur_Force_Mec = Region[ { Force } ];
-/*
- Signification of the abstract regions:
- Vol_Elast_Mec Elastic domain
- Vol_Force_Mec Region with imposed volumic force
- Sur_Force_Mec Surface with imposed surface traction
- Sur_Clamp_Mec Surface with imposed zero displacements (all components)
-*/
-}
-
-Function {
- /* Material coefficients.
- No need to define them regionwise here ( E[{Wrench}] = ... ; )
- as there is only one region in this model. */
- E[] = Young;
- nu[] = Poisson;
- /* Components of the volumic force applied to the region "Vol_Force_Mec"
- Gravity could be defined here ( force_y[] = 7000*9.81; ) ; */
- force_x[] = 0;
- force_y[] = 0;
- /* Components of the surface traction force applied to the region "Sur_Force_Mec" */
- pressure_x[] = 0;
- pressure_y[] = -AppliedForce/(SurfaceArea[]*Thickness); // downward vertical force
-}
-
-
-/* Hooke law
-
- The material law
-
- sigma_ij = C_ijkl epsilon_ij
-
- is represented in 2D by 4 2x2 tensors C_ij[], i,j=1,2
- depending on the Lamé coefficients of the isotropic linear material,
-
- lambda = E[]*nu[]/(1.+nu[])/(1.-2.*nu[]);
- mu = E[]/2./(1.+nu[]);
-
- as follows
-
- EPC: a[] = E/(1-nu^2) b[] = mu c[] = E nu/(1-nu^2)
- EPD: a[] = lambda + 2 mu b[] = mu c[] = lambda
- 3D: a[] = lambda + 2 mu b[] = mu c[] = lambda
-
- respectively for the 2D plane strain (EPD), 2D plane stress (EPS) and 3D cases.
-*/
-
-Function {
- Flag_EPC = 1;
- If(Flag_EPC) // Plane stress
- a[] = E[]/(1.-nu[]^2);
- c[] = E[]*nu[]/(1.-nu[]^2);
- Else // Plane strain or 3D
- a[] = E[]*(1.-nu[])/(1.+nu[])/(1.-2.*nu[]);
- c[] = E[]*nu[]/(1.+nu[])/(1.-2.*nu[]);
- EndIf
- b[] = E[]/2./(1.+nu[]);
-
- C_xx[] = Tensor[ a[],0 ,0 , 0 ,b[],0 , 0 ,0 ,b[] ];
- C_xy[] = Tensor[ 0 ,c[],0 , b[],0 ,0 , 0 ,0 ,0 ];
-
- C_yx[] = Tensor[ 0 ,b[],0 , c[],0 ,0 , 0 ,0 ,0 ];
- C_yy[] = Tensor[ b[],0 ,0 , 0 ,a[],0 , 0 ,0 ,b[] ];
-}
-
-/* Clamping boundary condition */
-Constraint {
- { Name Displacement_x;
- Case {
- { Region Sur_Clamp_Mec ; Type Assign ; Value 0; }
- }
- }
- { Name Displacement_y;
- Case {
- { Region Sur_Clamp_Mec ; Type Assign ; Value 0; }
- }
- }
-}
-
-/* As explained above, the displacement field is discretized
- as two scalar fields "ux" and "uy", which are the spatial components
- of the vector field "u" in a fixed Cartesian coordinate system.
-
- Boundary conditions like
-
- ux = ... ;
- uy = ... ;
-
- translate naturally into Dirichlet constraints
- on the scalar "ux" and "uy" FunctionSpaces.
- Conditions like, however,
-
- u . n = ux Cos [th] + uy Sin [th] = ... ;
-
- are less naturally accounted for within the "Grad u" formulation.
- Fortunately, they are rather uncommon.
-
- Finite element shape (triangles or quadrangles) makes no difference
- in the definition of the FunctionSpaces. The appropriate shape functions to be used
- are determined by GetDP at a much lower level on basis of the information
- contained in the *.msh file.
-
- Second order elements, on the other hand, are implemented in the hierarchical fashion
- by adding to the first order node-based shape functions
- a set of second order edge-based functions
- to complete a basis for 2d order polynomials on the reference element.
- */
-
-
-// Domain of definition of the "ux" and "uy" FunctionSpaces
-Group {
- Dom_H_u_Mec = Region[ { Vol_Elast_Mec,
- Sur_Force_Mec,
- Sur_Clamp_Mec} ];
-}
-
-Flag_Degree =
- DefineNumber[ 0, Name "Geometry/Use degree 2 (hierarch.)", Choices{0,1}, Visible 1];
-FE_Degree = ( Flag_Degree == 0 ) ? 1 : 2; // Convert flag value into polynomial degree
-
-FunctionSpace {
- { Name H_ux_Mec ; Type Form0 ;
- BasisFunction {
- { Name sxn ; NameOfCoef uxn ; Function BF_Node ;
- Support Dom_H_u_Mec ; Entity NodesOf[ All ] ; }
- If ( FE_Degree == 2 )
- { Name sxn2 ; NameOfCoef uxn2 ; Function BF_Node_2E ;
- Support Dom_H_u_Mec; Entity EdgesOf[ All ] ; }
- EndIf
- }
- Constraint {
- { NameOfCoef uxn ;
- EntityType NodesOf ; NameOfConstraint Displacement_x ; }
- If ( FE_Degree == 2 )
- { NameOfCoef uxn2 ;
- EntityType EdgesOf ; NameOfConstraint Displacement_x ; }
- EndIf
- }
- }
- { Name H_uy_Mec ; Type Form0 ;
- BasisFunction {
- { Name syn ; NameOfCoef uyn ; Function BF_Node ;
- Support Dom_H_u_Mec ; Entity NodesOf[ All ] ; }
- If ( FE_Degree == 2 )
- { Name syn2 ; NameOfCoef uyn2 ; Function BF_Node_2E ;
- Support Dom_H_u_Mec; Entity EdgesOf[ All ] ; }
- EndIf
- }
- Constraint {
- { NameOfCoef uyn ;
- EntityType NodesOf ; NameOfConstraint Displacement_y ; }
- If ( FE_Degree == 2 )
- { NameOfCoef uyn2 ;
- EntityType EdgesOf ; NameOfConstraint Displacement_y ; }
- EndIf
- }
- }
-}
-
-
-Jacobian {
- { Name Vol;
- Case {
- { Region All; Jacobian Vol; }
- }
- }
- { Name Sur;
- Case {
- { Region All; Jacobian Sur; }
- }
- }
-}
-
-/* Adapt the number of Gauss points to the polynomial degree of the finite elements
-is as simple as this: */
-If (FE_Degree == 1)
-Integration {
- { Name Gauss_v;
- Case {
- {Type Gauss;
- Case {
- { GeoElement Line ; NumberOfPoints 3; }
- { GeoElement Triangle ; NumberOfPoints 3; }
- { GeoElement Quadrangle ; NumberOfPoints 4; }
- }
- }
- }
- }
-}
-ElseIf (FE_Degree == 2)
-Integration {
- { Name Gauss_v;
- Case {
- {Type Gauss;
- Case {
- { GeoElement Line ; NumberOfPoints 5; }
- { GeoElement Triangle ; NumberOfPoints 7; }
- { GeoElement Quadrangle ; NumberOfPoints 7; }
- }
- }
- }
- }
-}
-EndIf
-
-Formulation {
- { Name Elast_u ; Type FemEquation ;
- Quantity {
- { Name ux ; Type Local ; NameOfSpace H_ux_Mec ; }
- { Name uy ; Type Local ; NameOfSpace H_uy_Mec ; }
- }
- Equation {
- Galerkin { [ -C_xx[] * Dof{d ux}, {d ux} ] ;
- In Vol_Elast_Mec ; Jacobian Vol ; Integration Gauss_v ; }
- Galerkin { [ -C_xy[] * Dof{d uy}, {d ux} ] ;
- In Vol_Elast_Mec ; Jacobian Vol ; Integration Gauss_v ; }
- Galerkin { [ -C_yx[] * Dof{d ux}, {d uy} ] ;
- In Vol_Elast_Mec ; Jacobian Vol ; Integration Gauss_v ; }
- Galerkin { [ -C_yy[] * Dof{d uy}, {d uy} ] ;
- In Vol_Elast_Mec ; Jacobian Vol ; Integration Gauss_v ; }
-
- Galerkin { [ force_x[] , {ux} ];
- In Vol_Force_Mec ; Jacobian Vol ; Integration Gauss_v ; }
- Galerkin { [ force_y[] , {uy} ];
- In Vol_Force_Mec ; Jacobian Vol ; Integration Gauss_v ; }
-
- Galerkin { [ pressure_x[] , {ux} ];
- In Sur_Force_Mec ; Jacobian Sur ; Integration Gauss_v ; }
- Galerkin { [ pressure_y[] , {uy} ];
- In Sur_Force_Mec ; Jacobian Sur ; Integration Gauss_v ; }
- }
- }
-}
-
-Resolution {
- { Name Elast_u ;
- System {
- { Name Sys_Mec ; NameOfFormulation Elast_u; }
- }
- Operation {
- InitSolution [Sys_Mec];
- Generate[Sys_Mec];
- Solve[Sys_Mec];
- SaveSolution[Sys_Mec] ;
- }
- }
-}
-
-PostProcessing {
- { Name Elast_u ; NameOfFormulation Elast_u ;
- PostQuantity {
- { Name u ; Value { Term { [ Vector[ {ux}, {uy}, 0 ]];
- In Vol_Elast_Mec ; Jacobian Vol ; } } }
- { Name uy ; Value { Term { [ 1e3*{uy} ];
- In Vol_Elast_Mec ; Jacobian Vol ; } } }
- { Name sig_xx ; Value { Term {
- [ CompX[ C_xx[]*{d ux} + C_xy[]*{d uy} ] ];
- In Vol_Elast_Mec ; Jacobian Vol ; } } }
- { Name sig_xy ; Value { Term {
- [ CompY[ C_xx[]*{d ux} + C_xy[]*{d uy} ] ];
- In Vol_Elast_Mec ; Jacobian Vol ; } } }
- { Name sig_yy ; Value { Term {
- [ CompY [ C_yx[]*{d ux} + C_yy[]*{d uy} ] ];
- In Vol_Elast_Mec ; Jacobian Vol ; } } }
- }
- }
-}
-
-
-
-PostOperation {
- { Name pos; NameOfPostProcessing Elast_u;
- Operation {
-
- If(FE_Degree == 1)
- Print[ sig_xx, OnElementsOf Wrench, File "sigxx.pos" ];
- Print[ u, OnElementsOf Wrench, File "u.pos" ];
- Else
- Print[ sig_xx, OnElementsOf Wrench, File "sigxx2.pos" ];
- Print[ u, OnElementsOf Wrench, File "u2.pos" ];
- EndIf
- Echo[ StrCat["l=PostProcessing.NbViews-1; ",
- "View[l].VectorType = 5; ",
- "View[l].ExternalView = l; ",
- "View[l].DisplacementFactor = 200; ",
- "View[l-1].IntervalsType = 3; "
- ],
- File "tmp.geo", LastTimeStepOnly] ;
- //Print[ sig_yy, OnElementsOf Wrench, File "sigyy.pos" ];
- //Print[ sig_xy, OnElementsOf Wrench, File "sigxy.pos" ];
- Print[ uy, OnPoint{probe_x, probe_y, 0},
- File > "deflection.pos", Format TimeTable,
- SendToServer "Solution/Deflection (computed) [mm]", Color "AliceBlue" ];
- }
- }
-}
-
-
-// Tell Gmsh which GetDP commands to execute when running the model.
-DefineConstant[
- R_ = {"Elast_u", Name "GetDP/1ResolutionChoices", Visible 0},
- P_ = {"pos", Name "GetDP/2PostOperationChoices", Visible 0},
- C_ = {"-solve -pos -v2", Name "GetDP/9ComputeCommand", Visible 0}
-];
-
+/* -------------------------------------------------------------------
+ Tutorial 3 : linear elastic model of a wrench
+
+ Features:
+ - "Grad u" GetDP specific formulation for linear elasticity
+ - first and second order elements
+ - triangular and quadrangular elements
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > wrench.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+/* Linear elasticity with GetDP:
+
+ GetDP has a peculiar way to deal with linear elasticity.
+ Instead of vector field "u = Vector[ ux, uy, uz ]",
+ the displacement field is regarded as two (2D case) or 3 (3D case) scalar fields.
+ Unlike conventional formulations, GetDP's formulation is written
+ in terms of the gradient "Grad u" of the displacement field,
+ which is a non-symmetric tensor, and the needed symmetrization
+ (to define the strain tensor and relate it to the stress tensor)
+ is done through the constitutive relationship (Hooke law).
+ The reason for this unusual formulation is to be able to use also for elastic problems
+ the powerful geometrical and homological kernel of GetDP,
+ which relies on the operators Grad, Curl and Div.
+
+ The "Grad u" formulation entails a small increase of assembly work
+ but makes in counterpart lots of geometrical features
+ implemented in GetDP (change of coordinates, function spaces, etc...)
+ applicable to elastic problems out-of-the-box,
+ since the scalar fields { ux, uy, uz } have exactly the same geometrical properties
+ as, e.g. a scalar electrip potential or a temperature field.
+*/
+
+
+Include "wrench2D_common.pro";
+
+Young = 1e9 *
+ DefineNumber[ 200, Name "Material/Young modulus [GPa]"];
+Poisson =
+ DefineNumber[ 0.3, Name "Material/Poisson coefficient []"];
+AppliedForce =
+ DefineNumber[ 100, Name "Material/Applied force [N]"];
+
+// Approximation of the maximum deflection by an analytical model:
+// Deflection = PL^3/(3EI) with I = Width^3*Thickness/12
+Deflection =
+ DefineNumber[4*AppliedForce*((LLength-0.018)/Width)^3/(Young*Thickness)*1e3,
+ Name "Solution/Deflection (analytical) [mm]", ReadOnly 1];
+
+Group {
+ // Physical regions: Give explicit labels to the regions defined in the .geo file
+ Wrench = Region[ 1 ];
+ Grip = Region[ 2 ];
+ Force = Region[ 3 ];
+
+ // Abstract regions:
+ Vol_Elast_Mec = Region[ { Wrench } ];
+ Vol_Force_Mec = Region[ { Wrench } ];
+ Sur_Clamp_Mec = Region[ { Grip } ];
+ Sur_Force_Mec = Region[ { Force } ];
+/*
+ Signification of the abstract regions:
+ Vol_Elast_Mec Elastic domain
+ Vol_Force_Mec Region with imposed volumic force
+ Sur_Force_Mec Surface with imposed surface traction
+ Sur_Clamp_Mec Surface with imposed zero displacements (all components)
+*/
+}
+
+Function {
+ /* Material coefficients.
+ No need to define them regionwise here ( E[{Wrench}] = ... ; )
+ as there is only one region in this model. */
+ E[] = Young;
+ nu[] = Poisson;
+ /* Components of the volumic force applied to the region "Vol_Force_Mec"
+ Gravity could be defined here ( force_y[] = 7000*9.81; ) ; */
+ force_x[] = 0;
+ force_y[] = 0;
+ /* Components of the surface traction force applied to the region "Sur_Force_Mec" */
+ pressure_x[] = 0;
+ pressure_y[] = -AppliedForce/(SurfaceArea[]*Thickness); // downward vertical force
+}
+
+
+/* Hooke law
+
+ The material law
+
+ sigma_ij = C_ijkl epsilon_ij
+
+ is represented in 2D by 4 2x2 tensors C_ij[], i,j=1,2
+ depending on the Lamé coefficients of the isotropic linear material,
+
+ lambda = E[]*nu[]/(1.+nu[])/(1.-2.*nu[]);
+ mu = E[]/2./(1.+nu[]);
+
+ as follows
+
+ EPC: a[] = E/(1-nu^2) b[] = mu c[] = E nu/(1-nu^2)
+ EPD: a[] = lambda + 2 mu b[] = mu c[] = lambda
+ 3D: a[] = lambda + 2 mu b[] = mu c[] = lambda
+
+ respectively for the 2D plane strain (EPD), 2D plane stress (EPS) and 3D cases.
+*/
+
+Function {
+ Flag_EPC = 1;
+ If(Flag_EPC) // Plane stress
+ a[] = E[]/(1.-nu[]^2);
+ c[] = E[]*nu[]/(1.-nu[]^2);
+ Else // Plane strain or 3D
+ a[] = E[]*(1.-nu[])/(1.+nu[])/(1.-2.*nu[]);
+ c[] = E[]*nu[]/(1.+nu[])/(1.-2.*nu[]);
+ EndIf
+ b[] = E[]/2./(1.+nu[]);
+
+ C_xx[] = Tensor[ a[],0 ,0 , 0 ,b[],0 , 0 ,0 ,b[] ];
+ C_xy[] = Tensor[ 0 ,c[],0 , b[],0 ,0 , 0 ,0 ,0 ];
+
+ C_yx[] = Tensor[ 0 ,b[],0 , c[],0 ,0 , 0 ,0 ,0 ];
+ C_yy[] = Tensor[ b[],0 ,0 , 0 ,a[],0 , 0 ,0 ,b[] ];
+}
+
+/* Clamping boundary condition */
+Constraint {
+ { Name Displacement_x;
+ Case {
+ { Region Sur_Clamp_Mec ; Type Assign ; Value 0; }
+ }
+ }
+ { Name Displacement_y;
+ Case {
+ { Region Sur_Clamp_Mec ; Type Assign ; Value 0; }
+ }
+ }
+}
+
+/* As explained above, the displacement field is discretized
+ as two scalar fields "ux" and "uy", which are the spatial components
+ of the vector field "u" in a fixed Cartesian coordinate system.
+
+ Boundary conditions like
+
+ ux = ... ;
+ uy = ... ;
+
+ translate naturally into Dirichlet constraints
+ on the scalar "ux" and "uy" FunctionSpaces.
+ Conditions like, however,
+
+ u . n = ux Cos [th] + uy Sin [th] = ... ;
+
+ are less naturally accounted for within the "Grad u" formulation.
+ Fortunately, they are rather uncommon.
+
+ Finite element shape (triangles or quadrangles) makes no difference
+ in the definition of the FunctionSpaces. The appropriate shape functions to be used
+ are determined by GetDP at a much lower level on basis of the information
+ contained in the *.msh file.
+
+ Second order elements, on the other hand, are implemented in the hierarchical fashion
+ by adding to the first order node-based shape functions
+ a set of second order edge-based functions
+ to complete a basis for 2d order polynomials on the reference element.
+ */
+
+
+// Domain of definition of the "ux" and "uy" FunctionSpaces
+Group {
+ Dom_H_u_Mec = Region[ { Vol_Elast_Mec,
+ Sur_Force_Mec,
+ Sur_Clamp_Mec} ];
+}
+
+Flag_Degree =
+ DefineNumber[ 0, Name "Geometry/Use degree 2 (hierarch.)", Choices{0,1}, Visible 1];
+FE_Degree = ( Flag_Degree == 0 ) ? 1 : 2; // Convert flag value into polynomial degree
+
+FunctionSpace {
+ { Name H_ux_Mec ; Type Form0 ;
+ BasisFunction {
+ { Name sxn ; NameOfCoef uxn ; Function BF_Node ;
+ Support Dom_H_u_Mec ; Entity NodesOf[ All ] ; }
+ If ( FE_Degree == 2 )
+ { Name sxn2 ; NameOfCoef uxn2 ; Function BF_Node_2E ;
+ Support Dom_H_u_Mec; Entity EdgesOf[ All ] ; }
+ EndIf
+ }
+ Constraint {
+ { NameOfCoef uxn ;
+ EntityType NodesOf ; NameOfConstraint Displacement_x ; }
+ If ( FE_Degree == 2 )
+ { NameOfCoef uxn2 ;
+ EntityType EdgesOf ; NameOfConstraint Displacement_x ; }
+ EndIf
+ }
+ }
+ { Name H_uy_Mec ; Type Form0 ;
+ BasisFunction {
+ { Name syn ; NameOfCoef uyn ; Function BF_Node ;
+ Support Dom_H_u_Mec ; Entity NodesOf[ All ] ; }
+ If ( FE_Degree == 2 )
+ { Name syn2 ; NameOfCoef uyn2 ; Function BF_Node_2E ;
+ Support Dom_H_u_Mec; Entity EdgesOf[ All ] ; }
+ EndIf
+ }
+ Constraint {
+ { NameOfCoef uyn ;
+ EntityType NodesOf ; NameOfConstraint Displacement_y ; }
+ If ( FE_Degree == 2 )
+ { NameOfCoef uyn2 ;
+ EntityType EdgesOf ; NameOfConstraint Displacement_y ; }
+ EndIf
+ }
+ }
+}
+
+
+Jacobian {
+ { Name Vol;
+ Case {
+ { Region All; Jacobian Vol; }
+ }
+ }
+ { Name Sur;
+ Case {
+ { Region All; Jacobian Sur; }
+ }
+ }
+}
+
+/* Adapt the number of Gauss points to the polynomial degree of the finite elements
+is as simple as this: */
+If (FE_Degree == 1)
+Integration {
+ { Name Gauss_v;
+ Case {
+ {Type Gauss;
+ Case {
+ { GeoElement Line ; NumberOfPoints 3; }
+ { GeoElement Triangle ; NumberOfPoints 3; }
+ { GeoElement Quadrangle ; NumberOfPoints 4; }
+ }
+ }
+ }
+ }
+}
+ElseIf (FE_Degree == 2)
+Integration {
+ { Name Gauss_v;
+ Case {
+ {Type Gauss;
+ Case {
+ { GeoElement Line ; NumberOfPoints 5; }
+ { GeoElement Triangle ; NumberOfPoints 7; }
+ { GeoElement Quadrangle ; NumberOfPoints 7; }
+ }
+ }
+ }
+ }
+}
+EndIf
+
+Formulation {
+ { Name Elast_u ; Type FemEquation ;
+ Quantity {
+ { Name ux ; Type Local ; NameOfSpace H_ux_Mec ; }
+ { Name uy ; Type Local ; NameOfSpace H_uy_Mec ; }
+ }
+ Equation {
+ Integral { [ -C_xx[] * Dof{d ux}, {d ux} ] ;
+ In Vol_Elast_Mec ; Jacobian Vol ; Integration Gauss_v ; }
+ Integral { [ -C_xy[] * Dof{d uy}, {d ux} ] ;
+ In Vol_Elast_Mec ; Jacobian Vol ; Integration Gauss_v ; }
+ Integral { [ -C_yx[] * Dof{d ux}, {d uy} ] ;
+ In Vol_Elast_Mec ; Jacobian Vol ; Integration Gauss_v ; }
+ Integral { [ -C_yy[] * Dof{d uy}, {d uy} ] ;
+ In Vol_Elast_Mec ; Jacobian Vol ; Integration Gauss_v ; }
+
+ Integral { [ force_x[] , {ux} ];
+ In Vol_Force_Mec ; Jacobian Vol ; Integration Gauss_v ; }
+ Integral { [ force_y[] , {uy} ];
+ In Vol_Force_Mec ; Jacobian Vol ; Integration Gauss_v ; }
+
+ Integral { [ pressure_x[] , {ux} ];
+ In Sur_Force_Mec ; Jacobian Sur ; Integration Gauss_v ; }
+ Integral { [ pressure_y[] , {uy} ];
+ In Sur_Force_Mec ; Jacobian Sur ; Integration Gauss_v ; }
+ }
+ }
+}
+
+Resolution {
+ { Name Elast_u ;
+ System {
+ { Name Sys_Mec ; NameOfFormulation Elast_u; }
+ }
+ Operation {
+ InitSolution [Sys_Mec];
+ Generate[Sys_Mec];
+ Solve[Sys_Mec];
+ SaveSolution[Sys_Mec] ;
+ }
+ }
+}
+
+PostProcessing {
+ { Name Elast_u ; NameOfFormulation Elast_u ;
+ PostQuantity {
+ { Name u ; Value { Term { [ Vector[ {ux}, {uy}, 0 ]];
+ In Vol_Elast_Mec ; Jacobian Vol ; } } }
+ { Name uy ; Value { Term { [ 1e3*{uy} ];
+ In Vol_Elast_Mec ; Jacobian Vol ; } } }
+ { Name sig_xx ; Value { Term {
+ [ CompX[ C_xx[]*{d ux} + C_xy[]*{d uy} ] ];
+ In Vol_Elast_Mec ; Jacobian Vol ; } } }
+ { Name sig_xy ; Value { Term {
+ [ CompY[ C_xx[]*{d ux} + C_xy[]*{d uy} ] ];
+ In Vol_Elast_Mec ; Jacobian Vol ; } } }
+ { Name sig_yy ; Value { Term {
+ [ CompY [ C_yx[]*{d ux} + C_yy[]*{d uy} ] ];
+ In Vol_Elast_Mec ; Jacobian Vol ; } } }
+ }
+ }
+}
+
+
+
+PostOperation {
+ { Name pos; NameOfPostProcessing Elast_u;
+ Operation {
+
+ If(FE_Degree == 1)
+ Print[ sig_xx, OnElementsOf Wrench, File "sigxx.pos" ];
+ Print[ u, OnElementsOf Wrench, File "u.pos" ];
+ Else
+ Print[ sig_xx, OnElementsOf Wrench, File "sigxx2.pos" ];
+ Print[ u, OnElementsOf Wrench, File "u2.pos" ];
+ EndIf
+ Echo[ StrCat["l=PostProcessing.NbViews-1; ",
+ "View[l].VectorType = 5; ",
+ "View[l].ExternalView = l; ",
+ "View[l].DisplacementFactor = 200; ",
+ "View[l-1].IntervalsType = 3; "
+ ],
+ File "tmp.geo", LastTimeStepOnly] ;
+ //Print[ sig_yy, OnElementsOf Wrench, File "sigyy.pos" ];
+ //Print[ sig_xy, OnElementsOf Wrench, File "sigxy.pos" ];
+ Print[ uy, OnPoint{probe_x, probe_y, 0},
+ File > "deflection.pos", Format TimeTable,
+ SendToServer "Solution/Deflection (computed) [mm]", Color "AliceBlue" ];
+ }
+ }
+}
+
+
+// Tell Gmsh which GetDP commands to execute when running the model.
+DefineConstant[
+ R_ = {"Elast_u", Name "GetDP/1ResolutionChoices", Visible 0},
+ P_ = {"pos", Name "GetDP/2PostOperationChoices", Visible 0},
+ C_ = {"-solve -pos -v2", Name "GetDP/9ComputeCommand", Visible 0}
+];
diff --git a/Elasticity/wrench2D_common.pro b/Elasticity/wrench2D_common.pro
index 578f64f..b9b045e 100644
--- a/Elasticity/wrench2D_common.pro
+++ b/Elasticity/wrench2D_common.pro
@@ -1,29 +1,29 @@
-// Some useful conversion coefficients
-mm = 1.e-3; // millimeters to meters
-cm = 1.e-2; // centimeters to meters
-in = 0.0254; // inches to meters
-deg = Pi/180.; // degrees to radians
-
-Refine =
- mm*DefineNumber[ 2, Name "Geometry/2Main characteristic length"];
-Recomb =
- DefineNumber[ 0, Name "Geometry/1Recombine", Choices{0,1}];
-Thickness =
- mm*DefineNumber[ 10, Name "Geometry/4Thickness (mm)"];
-Width =
- mm*DefineNumber[ 0.625*in/mm, Name "Geometry/5Arm Width (mm)"];
-LLength =
- cm*DefineNumber[ 6.0*in/cm, Name "Geometry/6Arm Length (cm)"];
-
-// Definition of the coordinates of the arm end
-// at which the maximal deflection will be evaluated.
-Inclination = 14*deg; // Arm angle with x-axis
-eps = 1e-6;
-probe_x = (LLength-eps)*Cos[Inclination];
-probe_y =-(LLength-eps)*Sin[Inclination];
-
-// a useful Print command to debug a model or communicate with the user
-Printf("Maximal deflection calculated at point (%f,%f)", probe_x, probe_y);
-
-
-
+// Some useful conversion coefficients
+mm = 1.e-3; // millimeters to meters
+cm = 1.e-2; // centimeters to meters
+in = 0.0254; // inches to meters
+deg = Pi/180.; // degrees to radians
+
+Refine =
+ mm*DefineNumber[ 2, Name "Geometry/2Main characteristic length"];
+Recomb =
+ DefineNumber[ 0, Name "Geometry/1Recombine", Choices{0,1}];
+Thickness =
+ mm*DefineNumber[ 10, Name "Geometry/4Thickness (mm)"];
+Width =
+ mm*DefineNumber[ 0.625*in/mm, Name "Geometry/5Arm Width (mm)"];
+LLength =
+ cm*DefineNumber[ 6.0*in/cm, Name "Geometry/6Arm Length (cm)"];
+
+// Definition of the coordinates of the arm end
+// at which the maximal deflection will be evaluated.
+Inclination = 14*deg; // Arm angle with x-axis
+eps = 1e-6;
+probe_x = (LLength-eps)*Cos[Inclination];
+probe_y =-(LLength-eps)*Sin[Inclination];
+
+// a useful Print command to debug a model or communicate with the user
+Printf("Maximal deflection calculated at point (%f,%f)", probe_x, probe_y);
+
+
+
diff --git a/Electrostatics/microstrip.geo b/Electrostatics/microstrip.geo
index 04ecbf5..0d0d855 100644
--- a/Electrostatics/microstrip.geo
+++ b/Electrostatics/microstrip.geo
@@ -1,58 +1,58 @@
-/* -------------------------------------------------------------------
- File "microstrip.geo"
-
- This file is the geometrical description used by Gmsh to produce the mesh
- file "microstrip.msh", which is read by GetDP when analysing the file
- "microstrip.pro".
- ------------------------------------------------------------------- */
-
-/* Definition of some parameters for geometrical dimensions, i.e. h (height of
- 'Diel1'), w (width of 'Line'), t (thickness of 'Line') xBox (width of the air
- box) and yBox (height of the air box) */
-
-h = 1.e-3 ; w = 4.72e-3 ; t = 0.035e-3 ;
-xBox = w/2. * 6. ; yBox = h * 12. ;
-
-/* Definition of parameters for local mesh dimensions */
-
-s = 1. ;
-p0 = h / 10. * s ;
-pLine0 = w/2. / 10. * s ; pLine1 = w/2. / 50. * s ;
-pxBox = xBox / 10. * s ; pyBox = yBox / 8. * s ;
-
-/* Definition of gemetrical points */
-
-Point(1) = { 0 , 0, 0, p0} ;
-Point(2) = { xBox, 0, 0, pxBox} ;
-Point(3) = { xBox, h, 0, pxBox} ;
-Point(4) = { 0 , h, 0, pLine0} ;
-Point(5) = { w/2., h, 0, pLine1} ;
-Point(6) = { 0 , h+t, 0, pLine0} ;
-Point(7) = { w/2., h+t, 0, pLine1} ;
-Point(8) = { 0 , yBox, 0, pyBox} ;
-Point(9) = { xBox, yBox, 0, pyBox} ;
-
-/* Definition of gemetrical lines */
-
-Line(1) = {1,2}; Line(2) = {2,3}; Line(3) = {3,9};
-Line(4) = {9,8}; Line(5) = {8,6}; Line(7) = {4,1};
-Line(8) = {5,3}; Line(9) = {4,5}; Line(10) = {6,7};
-Line(11) = {5,7};
-
-/* Definition of geometrical surfaces */
-
-Curve Loop(12) = {1, 2, -8, -9, 7}; Plane Surface(13) = {12};
-Curve Loop(14) = {10,-11,8,3,4,5}; Plane Surface(15) = {14};
-
-/* Definition of Physical entities. The definition of Physical entities
- (Surfaces and Curves) tells Gmsh the elements and associated region numbers
- that have to be saved in the mesh file 'microstrip.msh'. For example, Region
- 111 is made of the triangle elements of the geometric surface 13, whereas
- Region 121 is made of line elements of the geometric curves 9, 10 and 11. */
-
-Physical Surface("Air", 101) = {15};
-Physical Surface("Dielectric", 111) = {13};
-
-Physical Curve("Ground", 120) = {1} ;
-Physical Curve("Electrode", 121) = {9,10,11} ;
-Physical Curve("Surface infinity", 130) = {2,3,4} ;
+/* -------------------------------------------------------------------
+ File "microstrip.geo"
+
+ This file is the geometrical description used by Gmsh to produce the mesh
+ file "microstrip.msh", which is read by GetDP when analysing the file
+ "microstrip.pro".
+ ------------------------------------------------------------------- */
+
+/* Definition of some parameters for geometrical dimensions, i.e. h (height of
+ 'Diel1'), w (width of 'Line'), t (thickness of 'Line') xBox (width of the air
+ box) and yBox (height of the air box) */
+
+h = 1.e-3 ; w = 4.72e-3 ; t = 0.035e-3 ;
+xBox = w/2. * 6. ; yBox = h * 12. ;
+
+/* Definition of parameters for local mesh dimensions */
+
+s = 1. ;
+p0 = h / 10. * s ;
+pLine0 = w/2. / 10. * s ; pLine1 = w/2. / 50. * s ;
+pxBox = xBox / 10. * s ; pyBox = yBox / 8. * s ;
+
+/* Definition of gemetrical points */
+
+Point(1) = { 0 , 0, 0, p0} ;
+Point(2) = { xBox, 0, 0, pxBox} ;
+Point(3) = { xBox, h, 0, pxBox} ;
+Point(4) = { 0 , h, 0, pLine0} ;
+Point(5) = { w/2., h, 0, pLine1} ;
+Point(6) = { 0 , h+t, 0, pLine0} ;
+Point(7) = { w/2., h+t, 0, pLine1} ;
+Point(8) = { 0 , yBox, 0, pyBox} ;
+Point(9) = { xBox, yBox, 0, pyBox} ;
+
+/* Definition of gemetrical lines */
+
+Line(1) = {1,2}; Line(2) = {2,3}; Line(3) = {3,9};
+Line(4) = {9,8}; Line(5) = {8,6}; Line(7) = {4,1};
+Line(8) = {5,3}; Line(9) = {4,5}; Line(10) = {6,7};
+Line(11) = {5,7};
+
+/* Definition of geometrical surfaces */
+
+Curve Loop(12) = {1, 2, -8, -9, 7}; Plane Surface(13) = {12};
+Curve Loop(14) = {10,-11,8,3,4,5}; Plane Surface(15) = {14};
+
+/* Definition of Physical entities. The definition of Physical entities
+ (Surfaces and Curves) tells Gmsh the elements and associated region numbers
+ that have to be saved in the mesh file 'microstrip.msh'. For example, Region
+ 111 is made of the triangle elements of the geometric surface 13, whereas
+ Region 121 is made of line elements of the geometric curves 9, 10 and 11. */
+
+Physical Surface("Air", 101) = {15};
+Physical Surface("Dielectric", 111) = {13};
+
+Physical Curve("Ground", 120) = {1} ;
+Physical Curve("Electrode", 121) = {9,10,11} ;
+Physical Curve("Surface infinity", 130) = {2,3,4} ;
diff --git a/Electrostatics/microstrip.pro b/Electrostatics/microstrip.pro
index bdf89a6..f194945 100644
--- a/Electrostatics/microstrip.pro
+++ b/Electrostatics/microstrip.pro
@@ -1,327 +1,324 @@
-/* -------------------------------------------------------------------
- Tutorial 1 : electrostatic field of a microstrip
-
- Features:
- - Physical and abstract regions
- - Scalar FunctionSpace with Dirichlet constraint
- - Galerkin term for stiffness matrix
-
- To compute the solution in a terminal:
- getdp microstrip -solve EleSta_v
- getdp microstrip -pos Map
- getdp microstrip -pos Cut
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > microstrip.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-/* In this first tutorial we consider the calculation of the electric field
- given a static distribution of electric potential. This corresponds to an
- "electrostatic" physical model, obtained by combining the time-invariant
- Maxwell-Ampere equation (Curl e = 0, with e the electric field) with Gauss'
- law (Div d = rho, with d the displacement field and rho the charge density)
- and the dielectric constitutive law (d = epsilon e, with epsilon the
- dielectric permittivity).
-
- Since Curl e = 0, e can be derived from a scalar electric potential v, such
- that e = -Grad v. Plugging this potential in Gauss' law and using the
- constitutive law leads to a scalar Poisson equation in terms of the electric
- potential: -Div(epsilon Grad v) = rho.
-
- We consider here the special case where rho = 0, to model a conducting
- microstrip line on top of a dielectric substrate. A Dirichlet boundary
- condition sets the potential to 1 mV on the boundary of the microstrip line
- (called "Electrode" below) and 0 V on the ground. A homogeneous Neumann
- boundary condition (zero flux of the displacement field, i.e. n.d = 0) is
- imposed on the left boundary of the domain to account for the symmetry of the
- problem, as well as on the top and right boundaries that truncate the
- modelling domain. */
-
-Group {
- /* One starts by giving explicit meaningful names to the Physical regions
- defined in the "microstrip.msh" mesh file. We only use 2 volume regions and
- 2 surface regions in this model. */
-
- Air = Region[101];
- Diel1 = Region[111];
-
- Ground = Region[120];
- Electrode = Region[121];
-
- /* We now define abstract regions to be used below in the definition of the
- scalar electric potential formulation:
-
- Vol_Ele : volume where -Div(epsilon Grad v) = 0 is solved
- Sur_Neumann_Ele: surface where non homogeneous Neumann boundary conditions
- (on n.d == epsilon n.Grad v) are imposed
-
- Vol_xxx groups contain only volume elements of the mesh (triangles here).
- Sur_xxx groups contain only surface elements of the mesh (lines here).
-
- Since there are no non-homogeneous Neumann conditions in the model,
- Sur_Neumann_Ele is defined as empty.
- */
-
- Vol_Ele = Region[ {Air, Diel1} ];
- Sur_Neumann_Ele = Region[ {} ];
-}
-
-Function {
- /* Material laws (here the dielectric permittivity) are defined as piecewise
- functions (note the square brackets), in terms of the above defined
- physical regions. */
-
- eps0 = 8.854187818e-12;
- epsilon[Air] = 1. * eps0;
- epsilon[Diel1] = 9.8 * eps0;
-}
-
-Constraint {
- /* As for material laws, the Dirichlet boundary condition is defined
- piecewise. The constraint "Dirichlet_Ele" is invoked in the FunctionSpace
- below. */
-
- { Name Dirichlet_Ele; Type Assign;
- Case {
- { Region Ground; Value 0.; }
- { Region Electrode; Value 1.e-3; }
- }
- }
-}
-
-Group{
- /* The domain of definition of a FunctionSpace lists all regions on which a
- field is defined.
-
- Contrary to Vol_xxx and Sur_xxx regions, which contain only volume or
- surface regions, resp., domains of definition Dom_xxx regions may contain
- both volume and surface regions. Hence the use of the prefixes Vol_, Sur_
- and Dom_ to avoid confusions.*/
-
- Dom_Hgrad_v_Ele = Region[ {Vol_Ele, Sur_Neumann_Ele} ];
-}
-
-FunctionSpace {
- /* The function space in which we shall pick the electric scalar potential "v"
- solution is definied by
- - a domain of definition (the "Support": "Dom_Hgrad_v_Ele")
- - a type ("Form0" means scalar field)
- - a set of scalar basis functions ("BF_Node" means nodal basis functions)
- - a set of entities to which the basis functions are associated ("Entity":
- here all the nodes of the domain of definition "NodesOf[All]")
- - a constraint (here the Dirichlet boundary conditions)
-
- The FE expansion of the unknown field "v" reads
-
- v(x,y) = Sum_k vn_k sn_k(x,y)
-
- where the "vn_k" are the nodal values (connectors) and "sn_k(x,y)" the
- nodal basis functions. Not all connectors are unknowns of the FE problem,
- due to the "Constraint", which assigns particular values to the nodes of
- the Ground and Electrode regions. GetDP deals with that automatically on
- basis of the definition of the FunctionSpace. */
-
- { Name Hgrad_v_Ele; Type Form0;
- BasisFunction {
- { Name sn; NameOfCoef vn; Function BF_Node;
- Support Dom_Hgrad_v_Ele; Entity NodesOf[ All ]; }
- // using "NodesOf[All]" instead of "NodesOf[Dom_Hgrad_v_Ele]" is an
- // optimization, which allows GetDP to not explicitly build the list of
- // all nodes
- }
- Constraint {
- { NameOfCoef vn; EntityType NodesOf; NameOfConstraint Dirichlet_Ele; }
- }
- }
-}
-
-Jacobian {
- /* Jacobians are used to specify the mapping between elements in the mesh and
- the reference elements (defined in standardized unit cells) over which
- integration is performed. "Vol" represents the classical 1-to-1 mapping
- between elements of identical geometrical dimension, i.e. in this case a
- reference triangle/quadrangle onto triangles/quadrangles in the z=0 plane
- (2D <-> 2D). "Sur" would be used to map the reference triangle/quadrangle
- onto triangles/quadrangles in a 3D space (2D <-> 3D), or to map the
- reference line segment onto segments in 2D space (1D <-> 2D). "Lin" would
- be used to map the reference line segment onto segments in 3D space (1D <->
- 3D). */
-
- { Name Vol ;
- Case {
- { Region All ; Jacobian Vol ; }
- }
- }
-}
-
-Integration {
- /* A Gauss quadrature rule with 4 points is used for all integrations below. */
-
- { Name Int ;
- Case { { Type Gauss ;
- Case { { GeoElement Triangle ; NumberOfPoints 4 ; }
- { GeoElement Quadrangle ; NumberOfPoints 4 ; } }
- }
- }
- }
-}
-
-Formulation {
- /* The syntax of the Formulation section is a harder nut to crack. So let's
- deal with it carefully.
-
- A GetDP Formulation encodes a so-called weak formulation of the original
- partial differential equation, i.e. of -Div(epsilon Grad v) = 0. This weak
- formulation involves finding v such that
-
- (-Div(epsilon Grad v) , v')_Vol_Ele = 0
-
- holds for all so-called "test-functions" v', where (.,.)_D denotes an inner
- product over the domain D. If the test-functions v' are differentiable,
- integration by parts using Green's identity leads to finding v such that
-
- (epsilon Grad v, Grad v')_Vol_Ele + (epsilon n.Grad v, v')_Sur_Neumann_Ele = 0
-
- holds for all v'.
-
- In our microstrip example the Neumann boundary term vanishes and we are
- looking for functions v in the function space Hgrad_v_Ele such that
-
- (epsilon Grad v, Grad v')_Vol_Ele = 0
-
- holds for all v', where the test functions v' are the same basis functions
- ("sn_k") as the ones used to interpolate the unknown potential v.
-
- The Galerkin statement in the Formulation is a symbolic representation of
- this weak formulation. It has got 4 semicolon separated arguments:
- * the density [.,.] to be integrated (note the square brackets instead of
- the parentheses), with the test-functions (always) after the comma
- * the domain of integration,
- * the Jacobian of the transformation reference element <-> real element,
- * the integration method to be used.
-
- In the density, braces around a quantity (such as "{v}") indicate that this
- quantity belongs to a FunctionSpace. Differential operators can be applied
- within braces (such as "{Grad v}"); in particular the symbol "d" represents
- the exterior derivative, and it is a synonym of "Grad" when applied to a
- scalar function (such as "{d v}").
-
- What can be a bit confusing is that the two comma-separated terms of the
- density are not interpreted exactly in the same way. Let us unravel this in
- detail.
-
- As the Galerkin method uses as test functions the basis functions "sn_k" of
- the unknown field "v", the second term in the density should be something
- like this [ ... , basis_functions_of {d v} ]. However, since the second
- term is always devoted to test functions, the operator "basis_functions_of"
- would always be there. It can therefore be made implicit, and, according
- to the GetDP syntax, it is omitted. So, one writes simply [ ... , {d v} ].
-
- The first term, on the other hand, can contain a much wider variety of
- expressions than the second one. In our case it should be expressed in
- terms of the FE expansion of "v" at the present system solution, i.e. when
- the coefficients vn_k in the expansion of "v = Sum_k vn_k sn_k" are
- unknown. This is indicated by prefixing the braces with "Dof", which leads
- to the following density:
-
- [ epsilon[] * Dof{d v} , {d v} ],
-
- a so-called bilinear term that will contribute to the stiffness matrix of
- the electrostatic problem at hand.
-
- Another option, which would not work here, is to evaluate the first
- argument with the last available already computed solution, i.e. simply
- perform the interpolation with known coefficients vn_k. For this the Dof
- prefix operator would be omitted and we would have:
-
- [ epsilon[] * {d v} , {d v} ],
-
- a so-called linear term that will contribute to the right-hand side of the
- linear system.
-
- Both choices are commonly used in different contexts, and we shall come
- back on this often in subsequent tutorials. */
- { Name Electrostatics_v; Type FemEquation;
- Quantity {
- { Name v; Type Local; NameOfSpace Hgrad_v_Ele; }
- }
- Equation {
- Galerkin { [ epsilon[] * Dof{d v} , {d v} ];
- In Vol_Ele; Jacobian Vol; Integration Int; }
- }
- }
-}
-
-Resolution {
- { Name EleSta_v;
- System {
- { Name Sys_Ele; NameOfFormulation Electrostatics_v; }
- }
- Operation {
- Generate[Sys_Ele]; Solve[Sys_Ele]; SaveSolution[Sys_Ele];
- }
- }
-}
-
-/* Post-processing is done in two parts.
-
- The first part defines, in terms of the Formulation, which itself refers to
- the FunctionSpace, a number of quantities that can be evaluated at the
- postprocessing stage. The three quantities defined here are:
- - the scalar vector potential,
- - the electric field,
- - the electric displacement.
-
- The second part consists in defining groups of post-processing operations,
- which can be invoked separately. The first group is invoked by default when
- Gmsh is run interactively. Each Operation specifies
- - a quantity to be eveluated,
- - the region on which the evaluation is done,
- - the name of the output file.
- The generated post-processing files are automatically displayed by Gmsh if
- the "Merge result automatically" option is enabled (which is the default). */
-
-PostProcessing {
- { Name EleSta_v; NameOfFormulation Electrostatics_v;
- Quantity {
- { Name v;
- Value {
- Local { [ {v} ];
- In Dom_Hgrad_v_Ele; Jacobian Vol; }
- }
- }
- { Name e;
- Value {
- Local { [ -{d v} ];
- In Dom_Hgrad_v_Ele; Jacobian Vol; }
- }
- }
- { Name d;
- Value {
- Local { [ -epsilon[] * {d v} ];
- In Dom_Hgrad_v_Ele; Jacobian Vol; }
- }
- }
- }
- }
-}
-
-e = 1.e-7; // tolerance to ensure that the cut is inside the simulation domain
-h = 2.e-3; // vertical position of the cut
-
-PostOperation {
- { Name Map; NameOfPostProcessing EleSta_v;
- Operation {
- Print [ v, OnElementsOf Dom_Hgrad_v_Ele, File "mStrip_v.pos" ];
- Print [ e, OnElementsOf Dom_Hgrad_v_Ele, File "mStrip_e.pos" ];
- Print [ e, OnLine {{e,h,0}{14.e-3,h,0}}{60}, File "Cut_e.pos" ];
- }
- }
- { Name Cut; NameOfPostProcessing EleSta_v;
- // same cut as above, with more points and exported in raw text format
- Operation {
- Print [ e, OnLine {{e,e,0}{14.e-3,e,0}} {500}, Format TimeTable, File "Cut_e.txt" ];
- }
- }
-}
+/* -------------------------------------------------------------------
+ Tutorial 1 : electrostatic field of a microstrip
+
+ Features:
+ - Physical and abstract regions
+ - Scalar FunctionSpace with Dirichlet constraint
+ - Galerkin term for stiffness matrix
+
+ To compute the solution in a terminal:
+ getdp microstrip -solve EleSta_v
+ getdp microstrip -pos Map
+ getdp microstrip -pos Cut
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > microstrip.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+/* In this first tutorial we consider the calculation of the electric field
+ given a static distribution of electric potential. This corresponds to an
+ "electrostatic" physical model, obtained by combining the time-invariant
+ Maxwell-Ampere equation (Curl e = 0, with e the electric field) with Gauss'
+ law (Div d = rho, with d the displacement field and rho the charge density)
+ and the dielectric constitutive law (d = epsilon e, with epsilon the
+ dielectric permittivity).
+
+ Since Curl e = 0, e can be derived from a scalar electric potential v, such
+ that e = -Grad v. Plugging this potential in Gauss' law and using the
+ constitutive law leads to a scalar Poisson equation in terms of the electric
+ potential: -Div(epsilon Grad v) = rho.
+
+ We consider here the special case where rho = 0, to model a conducting
+ microstrip line on top of a dielectric substrate. A Dirichlet boundary
+ condition sets the potential to 1 mV on the boundary of the microstrip line
+ (called "Electrode" below) and 0 V on the ground. A homogeneous Neumann
+ boundary condition (zero flux of the displacement field, i.e. n.d = 0) is
+ imposed on the left boundary of the domain to account for the symmetry of the
+ problem, as well as on the top and right boundaries that truncate the
+ modelling domain. */
+
+Group {
+ /* One starts by giving explicit meaningful names to the Physical regions
+ defined in the "microstrip.msh" mesh file. We only use 2 volume regions and
+ 2 surface regions in this model. */
+
+ Air = Region[101];
+ Diel1 = Region[111];
+
+ Ground = Region[120];
+ Electrode = Region[121];
+
+ /* We now define abstract regions to be used below in the definition of the
+ scalar electric potential formulation:
+
+ Vol_Ele : volume where -Div(epsilon Grad v) = 0 is solved
+ Sur_Neumann_Ele: surface where non homogeneous Neumann boundary conditions
+ (on n.d == epsilon n.Grad v) are imposed
+
+ Vol_xxx groups contain only volume elements of the mesh (triangles here).
+ Sur_xxx groups contain only surface elements of the mesh (lines here).
+
+ Since there are no non-homogeneous Neumann conditions in the model,
+ Sur_Neumann_Ele is defined as empty.
+ */
+
+ Vol_Ele = Region[ {Air, Diel1} ];
+ Sur_Neumann_Ele = Region[ {} ];
+}
+
+Function {
+ /* Material laws (here the dielectric permittivity) are defined as piecewise
+ functions (note the square brackets), in terms of the above defined
+ physical regions. */
+
+ eps0 = 8.854187818e-12;
+ epsilon[Air] = 1. * eps0;
+ epsilon[Diel1] = 9.8 * eps0;
+}
+
+Constraint {
+ /* As for material laws, the Dirichlet boundary condition is defined
+ piecewise. The constraint "Dirichlet_Ele" is invoked in the FunctionSpace
+ below. */
+
+ { Name Dirichlet_Ele; Type Assign;
+ Case {
+ { Region Ground; Value 0.; }
+ { Region Electrode; Value 1.e-3; }
+ }
+ }
+}
+
+Group{
+ /* The domain of definition of a FunctionSpace lists all regions on which a
+ field is defined.
+
+ Contrary to Vol_xxx and Sur_xxx regions, which contain only volume or
+ surface regions, resp., domains of definition Dom_xxx regions may contain
+ both volume and surface regions. Hence the use of the prefixes Vol_, Sur_
+ and Dom_ to avoid confusions.*/
+
+ Dom_Hgrad_v_Ele = Region[ {Vol_Ele, Sur_Neumann_Ele} ];
+}
+
+FunctionSpace {
+ /* The function space in which we shall pick the electric scalar potential "v"
+ solution is definied by
+ - a domain of definition (the "Support": "Dom_Hgrad_v_Ele")
+ - a type ("Form0" means scalar field)
+ - a set of scalar basis functions ("BF_Node" means nodal basis functions)
+ - a set of entities to which the basis functions are associated ("Entity":
+ here all the nodes of the domain of definition "NodesOf[All]")
+ - a constraint (here the Dirichlet boundary conditions)
+
+ The FE expansion of the unknown field "v" reads
+
+ v(x,y) = Sum_k vn_k sn_k(x,y)
+
+ where the "vn_k" are the nodal values (connectors) and "sn_k(x,y)" the
+ nodal basis functions. Not all connectors are unknowns of the FE problem,
+ due to the "Constraint", which assigns particular values to the nodes of
+ the Ground and Electrode regions. GetDP deals with that automatically on
+ basis of the definition of the FunctionSpace. */
+
+ { Name Hgrad_v_Ele; Type Form0;
+ BasisFunction {
+ { Name sn; NameOfCoef vn; Function BF_Node;
+ Support Dom_Hgrad_v_Ele; Entity NodesOf[ All ]; }
+ // using "NodesOf[All]" instead of "NodesOf[Dom_Hgrad_v_Ele]" is an
+ // optimization, which allows GetDP to not explicitly build the list of
+ // all nodes
+ }
+ Constraint {
+ { NameOfCoef vn; EntityType NodesOf; NameOfConstraint Dirichlet_Ele; }
+ }
+ }
+}
+
+Jacobian {
+ /* Jacobians are used to specify the mapping between elements in the mesh and
+ the reference elements (defined in standardized unit cells) over which
+ integration is performed. "Vol" represents the classical 1-to-1 mapping
+ between elements of identical geometrical dimension, i.e. in this case a
+ reference triangle/quadrangle onto triangles/quadrangles in the z=0 plane
+ (2D <-> 2D). "Sur" would be used to map the reference triangle/quadrangle
+ onto triangles/quadrangles in a 3D space (2D <-> 3D), or to map the
+ reference line segment onto segments in 2D space (1D <-> 2D). "Lin" would
+ be used to map the reference line segment onto segments in 3D space (1D <->
+ 3D). */
+
+ { Name Vol ;
+ Case {
+ { Region All ; Jacobian Vol ; }
+ }
+ }
+}
+
+Integration {
+ /* A Gauss quadrature rule with 4 points is used for all integrations below. */
+
+ { Name Int ;
+ Case { { Type Gauss ;
+ Case { { GeoElement Triangle ; NumberOfPoints 4 ; }
+ { GeoElement Quadrangle ; NumberOfPoints 4 ; } }
+ }
+ }
+ }
+}
+
+Formulation {
+ /* The syntax of the Formulation section is a harder nut to crack. So let's
+ deal with it carefully.
+
+ A GetDP Formulation encodes a so-called weak formulation of the original
+ partial differential equation, i.e. of -Div(epsilon Grad v) = 0. This weak
+ formulation involves finding v such that
+
+ (-Div(epsilon Grad v) , v')_Vol_Ele = 0
+
+ holds for all so-called "test-functions" v', where (.,.)_D denotes an inner
+ product over the domain D. If the test-functions v' are differentiable,
+ integration by parts using Green's identity leads to finding v such that
+
+ (epsilon Grad v, Grad v')_Vol_Ele + (epsilon n.Grad v, v')_Bnd_Vol_Ele = 0
+
+ holds for all v', where Bnd_Vol_Ele is the boundary of Vol_Ele. In our
+ microstrip example this surface term vanishes, as either there is no test
+ function v' (on the Dirichlet boundary) or the "epsilon n.Grad v" is zero
+ (on the homogeneous Neumann boundary). We are thus eventually looking for
+ functions v in the function space Hgrad_v_Ele such that
+
+ (epsilon Grad v, Grad v')_Vol_Ele = 0
+
+ holds for all v'. Finally, our choice here is to use a Gakerkin method,
+ where the test functions v' are the same basis functions ("sn_k") as the
+ ones used to interpolate the unknown potential v.
+
+ The "Integral" statement in the Formulation is a symbolic representation of
+ this weak formulation. It has got 4 semicolon separated arguments:
+ * the density [.,.] to be integrated (note the square brackets instead of
+ the parentheses), with the test-functions (always) after the comma
+ * the domain of integration,
+ * the Jacobian of the transformation reference element <-> real element,
+ * the integration method to be used.
+
+ In the density, braces around a quantity (such as "{v}") indicate that this
+ quantity belongs to a FunctionSpace. Differential operators can be applied
+ within braces (such as "{Grad v}"); in particular the symbol "d" represents
+ the exterior derivative, and it is a synonym of "Grad" when applied to a
+ scalar function (such as "{d v}").
+
+ What can be a bit confusing is that the two comma-separated terms of the
+ density are not interpreted exactly in the same way. Let us unravel this in
+ detail.
+
+ As the Galerkin method uses as test functions the same basis functions
+ "sn_k" as for the unknown field "v", the second term in the density should
+ be something like this [ ... , basis_functions_of {d v} ]. However, since
+ the second term is always devoted to test functions, the operator
+ "basis_functions_of" would always be there. It can therefore be made
+ implicit, and, according to the GetDP syntax, it is omitted. So, one writes
+ simply [ ... , {d v} ].
+
+ The first term, on the other hand, can contain a much wider variety of
+ expressions than the second one. In our case it should be expressed in
+ terms of the FE expansion of "v" at the present system solution, i.e. when
+ the coefficients vn_k in the expansion of "v = Sum_k vn_k sn_k" are
+ unknown. This is indicated by prefixing the braces with "Dof", which leads
+ to the following density:
+
+ [ epsilon[] * Dof{d v} , {d v} ],
+
+ a so-called bilinear term that will contribute to the stiffness matrix of
+ the electrostatic problem at hand.
+
+ Another option, which would not work here, is to evaluate the first
+ argument with the last available already computed solution, i.e. simply
+ perform the interpolation with known coefficients vn_k. For this the Dof
+ prefix operator would be omitted and we would have:
+
+ [ epsilon[] * {d v} , {d v} ],
+
+ a so-called linear term that will contribute to the right-hand side of the
+ linear system.
+
+ Both choices are commonly used in different contexts, and we shall come
+ back on this often in subsequent tutorials. */
+ { Name Electrostatics_v; Type FemEquation;
+ Quantity {
+ { Name v; Type Local; NameOfSpace Hgrad_v_Ele; }
+ }
+ Equation {
+ Integral { [ epsilon[] * Dof{d v} , {d v} ];
+ In Vol_Ele; Jacobian Vol; Integration Int; }
+ }
+ }
+}
+
+Resolution {
+ { Name EleSta_v;
+ System {
+ { Name Sys_Ele; NameOfFormulation Electrostatics_v; }
+ }
+ Operation {
+ Generate[Sys_Ele]; Solve[Sys_Ele]; SaveSolution[Sys_Ele];
+ }
+ }
+}
+
+/* Post-processing is done in two parts.
+
+ The first part defines, in terms of the Formulation, which itself refers to
+ the FunctionSpace, a number of quantities that can be evaluated at the
+ postprocessing stage. The three quantities defined here are:
+ - the scalar vector potential,
+ - the electric field,
+ - the electric displacement.
+
+ The second part consists in defining groups of post-processing operations,
+ which can be invoked separately. The first group is invoked by default when
+ Gmsh is run interactively. Each Operation specifies
+ - a quantity to be eveluated,
+ - the region on which the evaluation is done,
+ - the name of the output file.
+ The generated post-processing files are automatically displayed by Gmsh if
+ the "Merge result automatically" option is enabled (which is the default). */
+
+PostProcessing {
+ { Name EleSta_v; NameOfFormulation Electrostatics_v;
+ Quantity {
+ { Name v; Value {
+ Local { [ {v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
+ }
+ }
+ { Name e; Value {
+ Local { [ -{d v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
+ }
+ }
+ { Name d; Value {
+ Local { [ -epsilon[] * {d v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
+ }
+ }
+ }
+ }
+}
+
+e = 1.e-7; // tolerance to ensure that the cut is inside the simulation domain
+h = 2.e-3; // vertical position of the cut
+
+PostOperation {
+ { Name Map; NameOfPostProcessing EleSta_v;
+ Operation {
+ Print [ v, OnElementsOf Dom_Hgrad_v_Ele, File "mStrip_v.pos" ];
+ Print [ e, OnElementsOf Dom_Hgrad_v_Ele, File "mStrip_e.pos" ];
+ Print [ e, OnLine {{e,h,0}{14.e-3,h,0}}{60}, File "Cut_e.pos" ];
+ }
+ }
+ { Name Cut; NameOfPostProcessing EleSta_v;
+ // same cut as above, with more points and exported in raw text format
+ Operation {
+ Print [ e, OnLine {{e,e,0}{14.e-3,e,0}} {500}, Format TimeTable, File "Cut_e.txt" ];
+ }
+ }
+}
diff --git a/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro b/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro
index 3a05f85..e0122eb 100644
--- a/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro
+++ b/Magnetodynamics/Lib_MagStaDyn_av_2D_Cir.pro
@@ -1,468 +1,468 @@
-// This is a template .pro file containing a general formulation for 2D
-// magnetostatic and magnetodynamic problems in terms of the magnetic vector
-// potential a (potentially coupled with the electric scalar potential v), with
-// optional circuit coupling.
-
-// Below are definitions of the constants (inside "DefineConstant"), groups
-// (inside "DefineGroup") and functions (inside "DefineFunction") that can be
-// redefined from outside this template.
-
-DefineConstant[
- Flag_FrequencyDomain = 1, // frequency-domain or time-domain simulation
- Flag_CircuitCoupling = 0 // consider coupling with external electric circuit
- CoefPower = 0.5, // coefficient for power calculations
- Freq = 50, // frequency (for harmonic simulations)
- TimeInit = 0, // intial time (for time-domain simulations)
- TimeFinal = 1/50, // final time (for time-domain simulations)
- DeltaTime = 1/500, // time step (for time-domain simulations)
- InterpolationOrder = 1 // finite element order
- Val_Rint = 0, // interior radius of annulus shell transformation region (VolInf_Mag)
- Val_Rext = 0 // exterior radius of annulus shell transformation region (VolInf_Mag)
-];
-
-Group {
- DefineGroup[
- VolCC_Mag, // the non-conducting part
- VolC_Mag, // the conducting part
- VolV_Mag, // a moving conducting part, with invariant mesh
- VolM_Mag, // permanent magnets
- VolS0_Mag, // current source domain with imposed current densities js0
- VolS_Mag, // current source domain with imposed current, imposed voltage or
- // circuit coupling
- VolInf_Mag, // annulus where a infinite shell transformation is applied
- SurFluxTube_Mag, // boundary with Neumann BC
- SurPerfect_Mag, // boundary of perfect conductors (i.e. non-meshed)
- SurImped_Mag // boundary of conductors approximated by a surface impedance
- // (i.e. non-meshed)
- ];
- If(Flag_CircuitCoupling)
- DefineGroup[
- SourceV_Cir, // voltage sources
- SourceI_Cir, // current sources
- Resistance_Cir, // resistors (linear)
- Inductance_Cir, // inductors
- Capacitance_Cir, // capacitors
- Diode_Cir // diodes (treated as nonlinear resistors)
- ];
- EndIf
-}
-
-Function {
- DefineFunction[
- nu, // reluctivity (in Vol_Mag)
- sigma, // conductivity (in VolC_Mag and VolS_Mag)
- br, // remanent magnetic flux density (in VolM_Mag)
- js0, // source current density (in VolS0_Mag)
- nxh, // n x magnetic field (on SurFluxTube_Mag)
- Velocity, // velocity of moving part VolV_Moving
- Ns, // number of turns (in VolS_Mag)
- Sc, // cross-section of windings (in VolS_Mag)
- CoefGeos, // geometrical coefficient for 2D or 2D axi model
- Ysur // surface admittance (inverse of surface impedance Zsur) on SurImped_Mag
- ];
- If(Flag_CircuitCoupling)
- DefineFunction[
- Resistance, // resistance values
- Inductance, // inductance values
- Capacitance // capacitance values
- ];
- EndIf
-}
-
-// End of definitions.
-
-Group{
- // all volumes
- Vol_Mag = Region[ {VolCC_Mag, VolC_Mag, VolV_Mag, VolM_Mag, VolS0_Mag, VolS_Mag} ];
- // all volumes + surfaces on which integrals will be computed
- VolWithSur_Mag = Region[ {Vol_Mag, SurFluxTube_Mag, SurPerfect_Mag, SurImped_Mag} ];
- If(Flag_CircuitCoupling)
- // all circuit impedances
- DomainZ_Cir = Region[ {Resistance_Cir, Inductance_Cir, Capacitance_Cir} ];
- // all circuit sources
- DomainSource_Cir = Region[ {SourceV_Cir, SourceI_Cir} ];
- // all circuit elements
- Domain_Cir = Region[ {DomainZ_Cir, DomainSource_Cir} ];
- EndIf
-}
-
-Jacobian {
- { Name Vol;
- Case {
- { Region VolInf_Mag ;
- Jacobian VolSphShell {Val_Rint, Val_Rext} ; }
- { Region All; Jacobian Vol; }
- }
- }
- { Name Sur;
- Case {
- { Region All; Jacobian Sur; }
- }
- }
-}
-
-Integration {
- { Name Gauss_v;
- Case {
- { Type Gauss;
- Case {
- { GeoElement Point; NumberOfPoints 1; }
- { GeoElement Line; NumberOfPoints 5; }
- { GeoElement Triangle; NumberOfPoints 7; }
- { GeoElement Quadrangle; NumberOfPoints 4; }
- { GeoElement Tetrahedron; NumberOfPoints 15; }
- { GeoElement Hexahedron; NumberOfPoints 14; }
- { GeoElement Prism; NumberOfPoints 21; }
- }
- }
- }
- }
-}
-
-// Same FunctionSpace for both static and dynamic formulations
-FunctionSpace {
- { Name Hcurl_a_2D; Type Form1P; // 1-form (circulations) on edges
- // perpendicular to the plane of study
- BasisFunction {
- // \vec{a}(x) = \sum_{n \in N(Domain)} a_n \vec{s}_n(x)
- // without nodes on perfect conductors (where a is constant)
- { Name s_n; NameOfCoef a_n; Function BF_PerpendicularEdge;
- Support VolWithSur_Mag; Entity NodesOf[All, Not SurPerfect_Mag]; }
-
- // global basis function on boundary of perfect conductors
- { Name s_skin; NameOfCoef a_skin; Function BF_GroupOfPerpendicularEdges;
- Support VolWithSur_Mag; Entity GroupsOfNodesOf[SurPerfect_Mag]; }
-
- // additional basis functions for 2nd order interpolation
- If(InterpolationOrder == 2)
- { Name s_e; NameOfCoef a_e; Function BF_PerpendicularEdge_2E;
- Support Vol_Mag; Entity EdgesOf[All]; }
- EndIf
- }
- GlobalQuantity {
- { Name A; Type AliasOf; NameOfCoef a_skin; }
- { Name I; Type AssociatedWith; NameOfCoef a_skin; }
- }
- Constraint {
- { NameOfCoef a_n;
- EntityType NodesOf; NameOfConstraint MagneticVectorPotential_2D; }
-
- { NameOfCoef I;
- EntityType GroupsOfNodesOf; NameOfConstraint Current_2D; }
-
- If(InterpolationOrder == 2)
- { NameOfCoef a_e;
- EntityType EdgesOf; NameOfConstraint MagneticVectorPotential_2D_0; }
- EndIf
- }
- }
-}
-
-FunctionSpace {
- // Gradient of Electric scalar potential (2D)
- { Name Hregion_u_2D; Type Form1P; // same as for \vec{a}
- BasisFunction {
- { Name sr; NameOfCoef ur; Function BF_RegionZ;
- // constant vector (over the region) with nonzero z-component only
- Support Region[{VolC_Mag, SurImped_Mag}];
- Entity Region[{VolC_Mag, SurImped_Mag}]; }
- }
- GlobalQuantity {
- { Name U; Type AliasOf; NameOfCoef ur; }
- { Name I; Type AssociatedWith; NameOfCoef ur; }
- }
- Constraint {
- { NameOfCoef U;
- EntityType Region; NameOfConstraint Voltage_2D; }
- { NameOfCoef I;
- EntityType Region; NameOfConstraint Current_2D; }
- }
- }
-
- // Current in stranded coil (2D)
- { Name Hregion_i_2D; Type Vector;
- BasisFunction {
- { Name sr; NameOfCoef ir; Function BF_RegionZ;
- Support VolS_Mag; Entity VolS_Mag; }
- }
- GlobalQuantity {
- { Name Is; Type AliasOf; NameOfCoef ir; }
- { Name Us; Type AssociatedWith; NameOfCoef ir; }
- }
- Constraint {
- { NameOfCoef Us;
- EntityType Region; NameOfConstraint Voltage_2D; }
- { NameOfCoef Is;
- EntityType Region; NameOfConstraint Current_2D; }
- }
- }
-}
-
-If(Flag_CircuitCoupling)
- // UZ and IZ for impedances
- FunctionSpace {
- { Name Hregion_Z; Type Scalar;
- BasisFunction {
- { Name sr; NameOfCoef ir; Function BF_Region;
- Support Domain_Cir; Entity Domain_Cir; }
- }
- GlobalQuantity {
- { Name Iz; Type AliasOf; NameOfCoef ir; }
- { Name Uz; Type AssociatedWith; NameOfCoef ir; }
- }
- Constraint {
- { NameOfCoef Uz;
- EntityType Region; NameOfConstraint Voltage_Cir; }
- { NameOfCoef Iz;
- EntityType Region; NameOfConstraint Current_Cir; }
- }
- }
- }
-EndIf
-
-
-// Static Formulation
-Formulation {
- { Name MagSta_a_2D; Type FemEquation;
- Quantity {
- { Name a; Type Local; NameOfSpace Hcurl_a_2D; }
- { Name ir; Type Local; NameOfSpace Hregion_i_2D; }
- }
- Equation {
- Galerkin { [ nu[] * Dof{d a} , {d a} ];
- In Vol_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Galerkin { [ -nu[] * br[] , {d a} ];
- In VolM_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Galerkin { [ -js0[] , {a} ];
- In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Galerkin { [ - (js0[]*Vector[0,0,1]) * Dof{ir} , {a} ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Galerkin { [ nxh[] , {a} ];
- In SurFluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
- }
- }
-}
-
-// Dynamic Formulation (eddy currents)
-Formulation {
- { Name MagDyn_a_2D; Type FemEquation;
- Quantity {
- { Name a; Type Local; NameOfSpace Hcurl_a_2D; }
- { Name A_floating; Type Global; NameOfSpace Hcurl_a_2D [A]; }
- { Name I_perfect; Type Global; NameOfSpace Hcurl_a_2D [I]; }
-
- { Name ur; Type Local; NameOfSpace Hregion_u_2D; }
- { Name I; Type Global; NameOfSpace Hregion_u_2D [I]; }
- { Name U; Type Global; NameOfSpace Hregion_u_2D [U]; }
-
- { Name ir; Type Local; NameOfSpace Hregion_i_2D; }
- { Name Us; Type Global; NameOfSpace Hregion_i_2D [Us]; }
- { Name Is; Type Global; NameOfSpace Hregion_i_2D [Is]; }
-
- If(Flag_CircuitCoupling)
- { Name Uz; Type Global; NameOfSpace Hregion_Z [Uz]; }
- { Name Iz; Type Global; NameOfSpace Hregion_Z [Iz]; }
- EndIf
- }
- Equation {
- Galerkin { [ nu[] * Dof{d a} , {d a} ];
- In Vol_Mag; Jacobian Vol; Integration Gauss_v; }
- Galerkin { [ -nu[] * br[] , {d a} ];
- In VolM_Mag; Jacobian Vol; Integration Gauss_v; }
-
- // Electric field e = -Dt[{a}]-{ur},
- // with {ur} = Grad v constant in each region of VolC
- Galerkin { DtDof [ sigma[] * Dof{a} , {a} ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
- Galerkin { [ sigma[] * Dof{ur} / CoefGeos[] , {a} ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Galerkin { [ - sigma[] * (Velocity[] /\ Dof{d a}) , {a} ];
- In VolV_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Galerkin { [ -js0[] , {a} ];
- In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Galerkin { [ nxh[] , {a} ];
- In SurFluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
-
- Galerkin { DtDof [ Ysur[] * Dof{a} , {a} ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
- Galerkin { [ Ysur[] * Dof{ur} / CoefGeos[] , {a} ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
-
- // When {ur} act as a test function, one obtains the circuits relations,
- // relating the voltage and the current of each region in VolC
- Galerkin { DtDof [ sigma[] * Dof{a} , {ur} ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
- Galerkin { [ sigma[] * Dof{ur} / CoefGeos[] , {ur} ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
- GlobalTerm { [ Dof{I} *(CoefGeos[]/Fabs[CoefGeos[]]) , {U} ]; In VolC_Mag; }
-
- Galerkin { DtDof [ Ysur[] * Dof{a} , {ur} ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
- Galerkin { [ Ysur[] * Dof{ur} / CoefGeos[] , {ur} ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
- GlobalTerm { [ Dof{I} *(CoefGeos[]/Fabs[CoefGeos[]]) , {U} ]; In SurImped_Mag; }
-
- // js[0] should be of the form: Ns[]/Sc[] * Vector[0,0,1]
- Galerkin { [ - (js0[]*Vector[0,0,1]) * Dof{ir} , {a} ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Galerkin { DtDof [ Ns[]/Sc[] * Dof{a} , {ir} ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
- Galerkin { [ Ns[]/Sc[] / sigma[] * (js0[]*Vector[0,0,1]) * Dof{ir} , {ir} ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
- GlobalTerm { [ Dof{Us} / CoefGeos[] , {Is} ]; In VolS_Mag; }
- // Attention: CoefGeo[.] = 2*Pi for Axi
-
- GlobalTerm { [ -Dof{I_perfect} , {A_floating} ]; In SurPerfect_Mag; }
-
- If(Flag_CircuitCoupling)
- GlobalTerm { NeverDt[ Dof{Uz} , {Iz} ]; In Resistance_Cir; }
- GlobalTerm { NeverDt[ Resistance[] * Dof{Iz} , {Iz} ]; In Resistance_Cir; }
-
- GlobalTerm { [ Dof{Uz} , {Iz} ]; In Inductance_Cir; }
- GlobalTerm { DtDof [ Inductance[] * Dof{Iz} , {Iz} ]; In Inductance_Cir; }
-
- GlobalTerm { NeverDt[ Dof{Iz} , {Iz} ]; In Capacitance_Cir; }
- GlobalTerm { DtDof [ Capacitance[] * Dof{Uz} , {Iz} ]; In Capacitance_Cir; }
-
- GlobalTerm { NeverDt[ Dof{Uz} , {Iz} ]; In Diode_Cir; }
- GlobalTerm { NeverDt[ Resistance[{Uz}] * Dof{Iz} , {Iz} ]; In Diode_Cir; }
-
- GlobalTerm { [ 0. * Dof{Iz} , {Iz} ]; In DomainSource_Cir; }
-
- GlobalEquation {
- Type Network; NameOfConstraint ElectricalCircuit;
- { Node {I}; Loop {U}; Equation {I}; In VolC_Mag; }
- { Node {Is}; Loop {Us}; Equation {Us}; In VolS_Mag; }
- { Node {Iz}; Loop {Uz}; Equation {Uz}; In Domain_Cir; }
- }
- EndIf
-
- }
- }
-}
-
-Resolution {
- { Name MagDyn_a_2D;
- System {
- { Name Sys; NameOfFormulation MagDyn_a_2D;
- If(Flag_FrequencyDomain)
- Type ComplexValue; Frequency Freq;
- EndIf
- }
- }
- Operation {
- If(Flag_FrequencyDomain)
- Generate[Sys]; Solve[Sys]; SaveSolution[Sys];
- Else
- InitSolution[Sys]; // provide initial condition
- TimeLoopTheta[TimeInit, TimeFinal, DeltaTime, 1.]{
- // Euler implicit (1) -- Crank-Nicolson (0.5)
- Generate[Sys]; Solve[Sys]; SaveSolution[Sys];
- }
- EndIf
- }
- }
- { Name MagSta_a_2D;
- System {
- { Name Sys; NameOfFormulation MagSta_a_2D; }
- }
- Operation {
- Generate[Sys]; Solve[Sys]; SaveSolution[Sys];
- }
- }
-}
-
-// Same PostProcessing for both static and dynamic formulations (both refer to
-// the same FunctionSpace from which the solution is obtained)
-PostProcessing {
- { Name MagDyn_a_2D; NameOfFormulation MagDyn_a_2D;
- PostQuantity {
- // In 2D, a is a vector with only a z-component: (0,0,az)
- { Name a; Value { Term { [ {a} ]; In Vol_Mag; Jacobian Vol; } } }
- // The equilines of az are field lines (giving the magnetic field direction)
- { Name az; Value { Term { [ CompZ[{a}] ]; In Vol_Mag; Jacobian Vol; } } }
- { Name b; Value { Term { [ {d a} ]; In Vol_Mag; Jacobian Vol; } } }
- { Name h; Value {
- Term { [ nu[] * {d a} ]; In Vol_Mag; Jacobian Vol; }
- Term { [ -nu[] * br[] ]; In VolM_Mag; Jacobian Vol; }
- }
- }
- { Name js; Value {
- Term { [ js0[] ]; In VolS0_Mag; Jacobian Vol; }
- Term { [ (js0[]*Vector[0,0,1])*{ir} ]; In VolS_Mag; Jacobian Vol; }
- Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; } // to force a vector result out of sources
- }
- }
- { Name j;
- // Only correct in MagDyn
- Value {
- Term { [ -sigma[] * (Dt[{a}]+{ur}/CoefGeos[]) ]; In VolC_Mag; Jacobian Vol; }
- Term { [ js0[] ]; In VolS0_Mag; Jacobian Vol; }
- Term { [ (js0[]*Vector[0,0,1])*{ir} ]; In VolS_Mag; Jacobian Vol; }
- Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; }
- // Current density in A/m
- Term { [ -Ysur[] * (Dt[{a}]+{ur}/CoefGeos[]) ]; In SurImped_Mag; Jacobian Sur; }
- }
- }
-
- { Name JouleLosses;
- Value {
- Integral { [ CoefPower * sigma[]*SquNorm[Dt[{a}]+{ur}/CoefGeos[]] ];
- In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
- Integral { [ CoefPower * 1./sigma[]*SquNorm[js0[]] ];
- In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Integral { [ CoefPower * 1./sigma[]*SquNorm[(js0[]*Vector[0,0,1])*{ir}] ];
- In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
-
- Integral { [ CoefPower * Ysur[]*SquNorm[Dt[{a}]+{ur}/CoefGeos[]] ];
- In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
- }
- }
-
- { Name U; Value {
- Term { [ {U} ]; In VolC_Mag; }
- Term { [ {Us} ]; In VolS_Mag; }
- If(Flag_CircuitCoupling)
- Term { [ {Uz} ]; In Domain_Cir; }
- EndIf
- }
- }
-
- { Name I; Value {
- Term { [ {I} ]; In VolC_Mag; }
- Term { [ {Is} ]; In VolS_Mag; }
- If(Flag_CircuitCoupling)
- Term { [ {Iz} ]; In Domain_Cir; }
- EndIf
- }
- }
-
- }
- }
-
- { Name MagSta_a_2D; NameOfFormulation MagSta_a_2D;
- PostQuantity {
- // In 2D, a is a vector with only a z-component: (0,0,az)
- { Name a; Value { Term { [ {a} ]; In Vol_Mag; Jacobian Vol; } } }
- // The equilines of az are field lines (giving the magnetic field direction)
- { Name az; Value { Term { [ CompZ[{a}] ]; In Vol_Mag; Jacobian Vol; } } }
- { Name b; Value { Term { [ {d a} ]; In Vol_Mag; Jacobian Vol; } } }
- { Name h; Value { Term { [ nu[] * {d a} ]; In Vol_Mag; Jacobian Vol; } } }
- { Name j;
- Value {
- Term { [ js0[] ]; In VolS0_Mag; Jacobian Vol; }
- Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; }
- }
- }
- }
- }
-}
+// This is a template .pro file containing a general formulation for 2D
+// magnetostatic and magnetodynamic problems in terms of the magnetic vector
+// potential a (potentially coupled with the electric scalar potential v), with
+// optional circuit coupling.
+
+// Below are definitions of the constants (inside "DefineConstant"), groups
+// (inside "DefineGroup") and functions (inside "DefineFunction") that can be
+// redefined from outside this template.
+
+DefineConstant[
+ Flag_FrequencyDomain = 1, // frequency-domain or time-domain simulation
+ Flag_CircuitCoupling = 0 // consider coupling with external electric circuit
+ CoefPower = 0.5, // coefficient for power calculations
+ Freq = 50, // frequency (for harmonic simulations)
+ TimeInit = 0, // intial time (for time-domain simulations)
+ TimeFinal = 1/50, // final time (for time-domain simulations)
+ DeltaTime = 1/500, // time step (for time-domain simulations)
+ InterpolationOrder = 1 // finite element order
+ Val_Rint = 0, // interior radius of annulus shell transformation region (VolInf_Mag)
+ Val_Rext = 0 // exterior radius of annulus shell transformation region (VolInf_Mag)
+];
+
+Group {
+ DefineGroup[
+ VolCC_Mag, // the non-conducting part
+ VolC_Mag, // the conducting part
+ VolV_Mag, // a moving conducting part, with invariant mesh
+ VolM_Mag, // permanent magnets
+ VolS0_Mag, // current source domain with imposed current densities js0
+ VolS_Mag, // current source domain with imposed current, imposed voltage or
+ // circuit coupling
+ VolInf_Mag, // annulus where a infinite shell transformation is applied
+ SurFluxTube_Mag, // boundary with Neumann BC
+ SurPerfect_Mag, // boundary of perfect conductors (i.e. non-meshed)
+ SurImped_Mag // boundary of conductors approximated by a surface impedance
+ // (i.e. non-meshed)
+ ];
+ If(Flag_CircuitCoupling)
+ DefineGroup[
+ SourceV_Cir, // voltage sources
+ SourceI_Cir, // current sources
+ Resistance_Cir, // resistors (linear)
+ Inductance_Cir, // inductors
+ Capacitance_Cir, // capacitors
+ Diode_Cir // diodes (treated as nonlinear resistors)
+ ];
+ EndIf
+}
+
+Function {
+ DefineFunction[
+ nu, // reluctivity (in Vol_Mag)
+ sigma, // conductivity (in VolC_Mag and VolS_Mag)
+ br, // remanent magnetic flux density (in VolM_Mag)
+ js0, // source current density (in VolS0_Mag)
+ nxh, // n x magnetic field (on SurFluxTube_Mag)
+ Velocity, // velocity of moving part VolV_Moving
+ Ns, // number of turns (in VolS_Mag)
+ Sc, // cross-section of windings (in VolS_Mag)
+ CoefGeos, // geometrical coefficient for 2D or 2D axi model
+ Ysur // surface admittance (inverse of surface impedance Zsur) on SurImped_Mag
+ ];
+ If(Flag_CircuitCoupling)
+ DefineFunction[
+ Resistance, // resistance values
+ Inductance, // inductance values
+ Capacitance // capacitance values
+ ];
+ EndIf
+}
+
+// End of definitions.
+
+Group{
+ // all volumes
+ Vol_Mag = Region[ {VolCC_Mag, VolC_Mag, VolV_Mag, VolM_Mag, VolS0_Mag, VolS_Mag} ];
+ // all volumes + surfaces on which integrals will be computed
+ VolWithSur_Mag = Region[ {Vol_Mag, SurFluxTube_Mag, SurPerfect_Mag, SurImped_Mag} ];
+ If(Flag_CircuitCoupling)
+ // all circuit impedances
+ DomainZ_Cir = Region[ {Resistance_Cir, Inductance_Cir, Capacitance_Cir} ];
+ // all circuit sources
+ DomainSource_Cir = Region[ {SourceV_Cir, SourceI_Cir} ];
+ // all circuit elements
+ Domain_Cir = Region[ {DomainZ_Cir, DomainSource_Cir} ];
+ EndIf
+}
+
+Jacobian {
+ { Name Vol;
+ Case {
+ { Region VolInf_Mag ;
+ Jacobian VolSphShell {Val_Rint, Val_Rext} ; }
+ { Region All; Jacobian Vol; }
+ }
+ }
+ { Name Sur;
+ Case {
+ { Region All; Jacobian Sur; }
+ }
+ }
+}
+
+Integration {
+ { Name Gauss_v;
+ Case {
+ { Type Gauss;
+ Case {
+ { GeoElement Point; NumberOfPoints 1; }
+ { GeoElement Line; NumberOfPoints 5; }
+ { GeoElement Triangle; NumberOfPoints 7; }
+ { GeoElement Quadrangle; NumberOfPoints 4; }
+ { GeoElement Tetrahedron; NumberOfPoints 15; }
+ { GeoElement Hexahedron; NumberOfPoints 14; }
+ { GeoElement Prism; NumberOfPoints 21; }
+ }
+ }
+ }
+ }
+}
+
+// Same FunctionSpace for both static and dynamic formulations
+FunctionSpace {
+ { Name Hcurl_a_2D; Type Form1P; // 1-form (circulations) on edges
+ // perpendicular to the plane of study
+ BasisFunction {
+ // \vec{a}(x) = \sum_{n \in N(Domain)} a_n \vec{s}_n(x)
+ // without nodes on perfect conductors (where a is constant)
+ { Name s_n; NameOfCoef a_n; Function BF_PerpendicularEdge;
+ Support VolWithSur_Mag; Entity NodesOf[All, Not SurPerfect_Mag]; }
+
+ // global basis function on boundary of perfect conductors
+ { Name s_skin; NameOfCoef a_skin; Function BF_GroupOfPerpendicularEdges;
+ Support VolWithSur_Mag; Entity GroupsOfNodesOf[SurPerfect_Mag]; }
+
+ // additional basis functions for 2nd order interpolation
+ If(InterpolationOrder == 2)
+ { Name s_e; NameOfCoef a_e; Function BF_PerpendicularEdge_2E;
+ Support Vol_Mag; Entity EdgesOf[All]; }
+ EndIf
+ }
+ GlobalQuantity {
+ { Name A; Type AliasOf; NameOfCoef a_skin; }
+ { Name I; Type AssociatedWith; NameOfCoef a_skin; }
+ }
+ Constraint {
+ { NameOfCoef a_n;
+ EntityType NodesOf; NameOfConstraint MagneticVectorPotential_2D; }
+
+ { NameOfCoef I;
+ EntityType GroupsOfNodesOf; NameOfConstraint Current_2D; }
+
+ If(InterpolationOrder == 2)
+ { NameOfCoef a_e;
+ EntityType EdgesOf; NameOfConstraint MagneticVectorPotential_2D_0; }
+ EndIf
+ }
+ }
+}
+
+FunctionSpace {
+ // Gradient of Electric scalar potential (2D)
+ { Name Hregion_u_2D; Type Form1P; // same as for \vec{a}
+ BasisFunction {
+ { Name sr; NameOfCoef ur; Function BF_RegionZ;
+ // constant vector (over the region) with nonzero z-component only
+ Support Region[{VolC_Mag, SurImped_Mag}];
+ Entity Region[{VolC_Mag, SurImped_Mag}]; }
+ }
+ GlobalQuantity {
+ { Name U; Type AliasOf; NameOfCoef ur; }
+ { Name I; Type AssociatedWith; NameOfCoef ur; }
+ }
+ Constraint {
+ { NameOfCoef U;
+ EntityType Region; NameOfConstraint Voltage_2D; }
+ { NameOfCoef I;
+ EntityType Region; NameOfConstraint Current_2D; }
+ }
+ }
+
+ // Current in stranded coil (2D)
+ { Name Hregion_i_2D; Type Vector;
+ BasisFunction {
+ { Name sr; NameOfCoef ir; Function BF_RegionZ;
+ Support VolS_Mag; Entity VolS_Mag; }
+ }
+ GlobalQuantity {
+ { Name Is; Type AliasOf; NameOfCoef ir; }
+ { Name Us; Type AssociatedWith; NameOfCoef ir; }
+ }
+ Constraint {
+ { NameOfCoef Us;
+ EntityType Region; NameOfConstraint Voltage_2D; }
+ { NameOfCoef Is;
+ EntityType Region; NameOfConstraint Current_2D; }
+ }
+ }
+}
+
+If(Flag_CircuitCoupling)
+ // UZ and IZ for impedances
+ FunctionSpace {
+ { Name Hregion_Z; Type Scalar;
+ BasisFunction {
+ { Name sr; NameOfCoef ir; Function BF_Region;
+ Support Domain_Cir; Entity Domain_Cir; }
+ }
+ GlobalQuantity {
+ { Name Iz; Type AliasOf; NameOfCoef ir; }
+ { Name Uz; Type AssociatedWith; NameOfCoef ir; }
+ }
+ Constraint {
+ { NameOfCoef Uz;
+ EntityType Region; NameOfConstraint Voltage_Cir; }
+ { NameOfCoef Iz;
+ EntityType Region; NameOfConstraint Current_Cir; }
+ }
+ }
+ }
+EndIf
+
+
+// Static Formulation
+Formulation {
+ { Name MagSta_a_2D; Type FemEquation;
+ Quantity {
+ { Name a; Type Local; NameOfSpace Hcurl_a_2D; }
+ { Name ir; Type Local; NameOfSpace Hregion_i_2D; }
+ }
+ Equation {
+ Integral { [ nu[] * Dof{d a} , {d a} ];
+ In Vol_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ -nu[] * br[] , {d a} ];
+ In VolM_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ -js0[] , {a} ];
+ In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ - (js0[]*Vector[0,0,1]) * Dof{ir} , {a} ];
+ In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ nxh[] , {a} ];
+ In SurFluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
+ }
+ }
+}
+
+// Dynamic Formulation (eddy currents)
+Formulation {
+ { Name MagDyn_a_2D; Type FemEquation;
+ Quantity {
+ { Name a; Type Local; NameOfSpace Hcurl_a_2D; }
+ { Name A_floating; Type Global; NameOfSpace Hcurl_a_2D [A]; }
+ { Name I_perfect; Type Global; NameOfSpace Hcurl_a_2D [I]; }
+
+ { Name ur; Type Local; NameOfSpace Hregion_u_2D; }
+ { Name I; Type Global; NameOfSpace Hregion_u_2D [I]; }
+ { Name U; Type Global; NameOfSpace Hregion_u_2D [U]; }
+
+ { Name ir; Type Local; NameOfSpace Hregion_i_2D; }
+ { Name Us; Type Global; NameOfSpace Hregion_i_2D [Us]; }
+ { Name Is; Type Global; NameOfSpace Hregion_i_2D [Is]; }
+
+ If(Flag_CircuitCoupling)
+ { Name Uz; Type Global; NameOfSpace Hregion_Z [Uz]; }
+ { Name Iz; Type Global; NameOfSpace Hregion_Z [Iz]; }
+ EndIf
+ }
+ Equation {
+ Integral { [ nu[] * Dof{d a} , {d a} ];
+ In Vol_Mag; Jacobian Vol; Integration Gauss_v; }
+ Integral { [ -nu[] * br[] , {d a} ];
+ In VolM_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ // Electric field e = -Dt[{a}]-{ur},
+ // with {ur} = Grad v constant in each region of VolC
+ Integral { DtDof [ sigma[] * Dof{a} , {a} ];
+ In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+ Integral { [ sigma[] * Dof{ur} / CoefGeos[] , {a} ];
+ In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ - sigma[] * (Velocity[] /\ Dof{d a}) , {a} ];
+ In VolV_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ -js0[] , {a} ];
+ In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ nxh[] , {a} ];
+ In SurFluxTube_Mag; Jacobian Sur; Integration Gauss_v; }
+
+ Integral { DtDof [ Ysur[] * Dof{a} , {a} ];
+ In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+ Integral { [ Ysur[] * Dof{ur} / CoefGeos[] , {a} ];
+ In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+
+ // When {ur} act as a test function, one obtains the circuits relations,
+ // relating the voltage and the current of each region in VolC
+ Integral { DtDof [ sigma[] * Dof{a} , {ur} ];
+ In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+ Integral { [ sigma[] * Dof{ur} / CoefGeos[] , {ur} ];
+ In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+ GlobalTerm { [ Dof{I} *(CoefGeos[]/Fabs[CoefGeos[]]) , {U} ]; In VolC_Mag; }
+
+ Integral { DtDof [ Ysur[] * Dof{a} , {ur} ];
+ In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+ Integral { [ Ysur[] * Dof{ur} / CoefGeos[] , {ur} ];
+ In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+ GlobalTerm { [ Dof{I} *(CoefGeos[]/Fabs[CoefGeos[]]) , {U} ]; In SurImped_Mag; }
+
+ // js[0] should be of the form: Ns[]/Sc[] * Vector[0,0,1]
+ Integral { [ - (js0[]*Vector[0,0,1]) * Dof{ir} , {a} ];
+ In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { DtDof [ Ns[]/Sc[] * Dof{a} , {ir} ];
+ In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+ Integral { [ Ns[]/Sc[] / sigma[] * (js0[]*Vector[0,0,1]) * Dof{ir} , {ir} ];
+ In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+ GlobalTerm { [ Dof{Us} / CoefGeos[] , {Is} ]; In VolS_Mag; }
+ // Attention: CoefGeo[.] = 2*Pi for Axi
+
+ GlobalTerm { [ -Dof{I_perfect} , {A_floating} ]; In SurPerfect_Mag; }
+
+ If(Flag_CircuitCoupling)
+ GlobalTerm { NeverDt[ Dof{Uz} , {Iz} ]; In Resistance_Cir; }
+ GlobalTerm { NeverDt[ Resistance[] * Dof{Iz} , {Iz} ]; In Resistance_Cir; }
+
+ GlobalTerm { [ Dof{Uz} , {Iz} ]; In Inductance_Cir; }
+ GlobalTerm { DtDof [ Inductance[] * Dof{Iz} , {Iz} ]; In Inductance_Cir; }
+
+ GlobalTerm { NeverDt[ Dof{Iz} , {Iz} ]; In Capacitance_Cir; }
+ GlobalTerm { DtDof [ Capacitance[] * Dof{Uz} , {Iz} ]; In Capacitance_Cir; }
+
+ GlobalTerm { NeverDt[ Dof{Uz} , {Iz} ]; In Diode_Cir; }
+ GlobalTerm { NeverDt[ Resistance[{Uz}] * Dof{Iz} , {Iz} ]; In Diode_Cir; }
+
+ GlobalTerm { [ 0. * Dof{Iz} , {Iz} ]; In DomainSource_Cir; }
+
+ GlobalEquation {
+ Type Network; NameOfConstraint ElectricalCircuit;
+ { Node {I}; Loop {U}; Equation {I}; In VolC_Mag; }
+ { Node {Is}; Loop {Us}; Equation {Us}; In VolS_Mag; }
+ { Node {Iz}; Loop {Uz}; Equation {Uz}; In Domain_Cir; }
+ }
+ EndIf
+
+ }
+ }
+}
+
+Resolution {
+ { Name MagDyn_a_2D;
+ System {
+ { Name Sys; NameOfFormulation MagDyn_a_2D;
+ If(Flag_FrequencyDomain)
+ Type ComplexValue; Frequency Freq;
+ EndIf
+ }
+ }
+ Operation {
+ If(Flag_FrequencyDomain)
+ Generate[Sys]; Solve[Sys]; SaveSolution[Sys];
+ Else
+ InitSolution[Sys]; // provide initial condition
+ TimeLoopTheta[TimeInit, TimeFinal, DeltaTime, 1.]{
+ // Euler implicit (1) -- Crank-Nicolson (0.5)
+ Generate[Sys]; Solve[Sys]; SaveSolution[Sys];
+ }
+ EndIf
+ }
+ }
+ { Name MagSta_a_2D;
+ System {
+ { Name Sys; NameOfFormulation MagSta_a_2D; }
+ }
+ Operation {
+ Generate[Sys]; Solve[Sys]; SaveSolution[Sys];
+ }
+ }
+}
+
+// Same PostProcessing for both static and dynamic formulations (both refer to
+// the same FunctionSpace from which the solution is obtained)
+PostProcessing {
+ { Name MagDyn_a_2D; NameOfFormulation MagDyn_a_2D;
+ PostQuantity {
+ // In 2D, a is a vector with only a z-component: (0,0,az)
+ { Name a; Value { Term { [ {a} ]; In Vol_Mag; Jacobian Vol; } } }
+ // The equilines of az are field lines (giving the magnetic field direction)
+ { Name az; Value { Term { [ CompZ[{a}] ]; In Vol_Mag; Jacobian Vol; } } }
+ { Name b; Value { Term { [ {d a} ]; In Vol_Mag; Jacobian Vol; } } }
+ { Name h; Value {
+ Term { [ nu[] * {d a} ]; In Vol_Mag; Jacobian Vol; }
+ Term { [ -nu[] * br[] ]; In VolM_Mag; Jacobian Vol; }
+ }
+ }
+ { Name js; Value {
+ Term { [ js0[] ]; In VolS0_Mag; Jacobian Vol; }
+ Term { [ (js0[]*Vector[0,0,1])*{ir} ]; In VolS_Mag; Jacobian Vol; }
+ Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; } // to force a vector result out of sources
+ }
+ }
+ { Name j;
+ // Only correct in MagDyn
+ Value {
+ Term { [ -sigma[] * (Dt[{a}]+{ur}/CoefGeos[]) ]; In VolC_Mag; Jacobian Vol; }
+ Term { [ js0[] ]; In VolS0_Mag; Jacobian Vol; }
+ Term { [ (js0[]*Vector[0,0,1])*{ir} ]; In VolS_Mag; Jacobian Vol; }
+ Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; }
+ // Current density in A/m
+ Term { [ -Ysur[] * (Dt[{a}]+{ur}/CoefGeos[]) ]; In SurImped_Mag; Jacobian Sur; }
+ }
+ }
+
+ { Name JouleLosses;
+ Value {
+ Integral { [ CoefPower * sigma[]*SquNorm[Dt[{a}]+{ur}/CoefGeos[]] ];
+ In VolC_Mag; Jacobian Vol; Integration Gauss_v; }
+ Integral { [ CoefPower * 1./sigma[]*SquNorm[js0[]] ];
+ In VolS0_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ CoefPower * 1./sigma[]*SquNorm[(js0[]*Vector[0,0,1])*{ir}] ];
+ In VolS_Mag; Jacobian Vol; Integration Gauss_v; }
+
+ Integral { [ CoefPower * Ysur[]*SquNorm[Dt[{a}]+{ur}/CoefGeos[]] ];
+ In SurImped_Mag; Jacobian Sur; Integration Gauss_v; }
+ }
+ }
+
+ { Name U; Value {
+ Term { [ {U} ]; In VolC_Mag; }
+ Term { [ {Us} ]; In VolS_Mag; }
+ If(Flag_CircuitCoupling)
+ Term { [ {Uz} ]; In Domain_Cir; }
+ EndIf
+ }
+ }
+
+ { Name I; Value {
+ Term { [ {I} ]; In VolC_Mag; }
+ Term { [ {Is} ]; In VolS_Mag; }
+ If(Flag_CircuitCoupling)
+ Term { [ {Iz} ]; In Domain_Cir; }
+ EndIf
+ }
+ }
+
+ }
+ }
+
+ { Name MagSta_a_2D; NameOfFormulation MagSta_a_2D;
+ PostQuantity {
+ // In 2D, a is a vector with only a z-component: (0,0,az)
+ { Name a; Value { Term { [ {a} ]; In Vol_Mag; Jacobian Vol; } } }
+ // The equilines of az are field lines (giving the magnetic field direction)
+ { Name az; Value { Term { [ CompZ[{a}] ]; In Vol_Mag; Jacobian Vol; } } }
+ { Name b; Value { Term { [ {d a} ]; In Vol_Mag; Jacobian Vol; } } }
+ { Name h; Value { Term { [ nu[] * {d a} ]; In Vol_Mag; Jacobian Vol; } } }
+ { Name j;
+ Value {
+ Term { [ js0[] ]; In VolS0_Mag; Jacobian Vol; }
+ Term { [ Vector[0,0,0] ]; In Vol_Mag; Jacobian Vol; }
+ }
+ }
+ }
+ }
+}
diff --git a/Magnetodynamics/electromagnet.geo b/Magnetodynamics/electromagnet.geo
index 7bd410c..b24c084 100644
--- a/Magnetodynamics/electromagnet.geo
+++ b/Magnetodynamics/electromagnet.geo
@@ -1,54 +1,54 @@
-/* -------------------------------------------------------------------
- File "electromagnet.geo"
-
- This file is the geometrical description used by GMSH to produce
- the file "electromagnet.msh".
- ------------------------------------------------------------------- */
-
-dxCore = 50.e-3; dyCore = 100.e-3;
-xInd = 75.e-3; dxInd = 25.e-3; dyInd = 50.e-3;
-
-Include "electromagnet_common.pro";
-
-s = DefineNumber[1, Name "Model parameters/Global mesh size",
- Help "Reduce for finer mesh"];
-p0 = 12.e-3 *s;
-pCorex = 4.e-3 *s; pCorey0 = 8.e-3 *s; pCorey = 4.e-3 *s;
-pIndx = 5.e-3 *s; pIndy = 5.e-3 *s;
-pInt = 12.5e-3*s; pExt = 12.5e-3*s;
-
-Point(1) = {0,0,0,p0};
-Point(2) = {dxCore,0,0,pCorex};
-Point(3) = {dxCore,dyCore,0,pCorey};
-Point(4) = {0,dyCore,0,pCorey0};
-Point(5) = {xInd,0,0,pIndx};
-Point(6) = {xInd+dxInd,0,0,pIndx};
-Point(7) = {xInd+dxInd,dyInd,0,pIndy};
-Point(8) = {xInd,dyInd,0,pIndy};
-Point(9) = {rInt,0,0,pInt};
-Point(10) = {rExt,0,0,pExt};
-Point(11) = {0,rInt,0,pInt};
-Point(12) = {0,rExt,0,pExt};
-
-Line(1) = {1,2}; Line(2) = {2,5}; Line(3) = {5,6};
-Line(4) = {6,9}; Line(5) = {9,10}; Line(6) = {1,4};
-Line(7) = {4,11}; Line(8) = {11,12}; Line(9) = {2,3};
-Line(10) = {3,4}; Line(11) = {6,7}; Line(12) = {7,8};
-Line(13) = {8,5};
-
-Circle(14) = {9,1,11}; Circle(15) = {10,1,12};
-
-Line Loop(16) = {-6,1,9,10}; Plane Surface(17) = {16};
-Line Loop(18) = {11,12,13,3}; Plane Surface(19) = {18};
-Line Loop(20) = {7,-14,-4,11,12,13,-2,9,10}; Plane Surface(21) = {-20}; // "-" for orientation
-Line Loop(22) = {8,-15,-5,14}; Plane Surface(23) = {-22};
-
-Physical Surface(101) = {21}; /* Air */
-Physical Surface(102) = {17}; /* Core */
-Physical Surface(103) = {19}; /* Ind */
-Physical Surface(111) = {23}; /* AirInf */
-
-Physical Line(1100) = {1,2,3,4,5}; /* Surface ht = 0 */
-Physical Line(1101) = {6,7,8}; /* Surface bn = 0 */
-Physical Line(1102) = {15}; /* Surface Inf */
-
+/* -------------------------------------------------------------------
+ File "electromagnet.geo"
+
+ This file is the geometrical description used by GMSH to produce
+ the file "electromagnet.msh".
+ ------------------------------------------------------------------- */
+
+dxCore = 50.e-3; dyCore = 100.e-3;
+xInd = 75.e-3; dxInd = 25.e-3; dyInd = 50.e-3;
+
+Include "electromagnet_common.pro";
+
+s = DefineNumber[1, Name "Model parameters/Global mesh size",
+ Help "Reduce for finer mesh"];
+p0 = 12.e-3 *s;
+pCorex = 4.e-3 *s; pCorey0 = 8.e-3 *s; pCorey = 4.e-3 *s;
+pIndx = 5.e-3 *s; pIndy = 5.e-3 *s;
+pInt = 12.5e-3*s; pExt = 12.5e-3*s;
+
+Point(1) = {0,0,0,p0};
+Point(2) = {dxCore,0,0,pCorex};
+Point(3) = {dxCore,dyCore,0,pCorey};
+Point(4) = {0,dyCore,0,pCorey0};
+Point(5) = {xInd,0,0,pIndx};
+Point(6) = {xInd+dxInd,0,0,pIndx};
+Point(7) = {xInd+dxInd,dyInd,0,pIndy};
+Point(8) = {xInd,dyInd,0,pIndy};
+Point(9) = {rInt,0,0,pInt};
+Point(10) = {rExt,0,0,pExt};
+Point(11) = {0,rInt,0,pInt};
+Point(12) = {0,rExt,0,pExt};
+
+Line(1) = {1,2}; Line(2) = {2,5}; Line(3) = {5,6};
+Line(4) = {6,9}; Line(5) = {9,10}; Line(6) = {1,4};
+Line(7) = {4,11}; Line(8) = {11,12}; Line(9) = {2,3};
+Line(10) = {3,4}; Line(11) = {6,7}; Line(12) = {7,8};
+Line(13) = {8,5};
+
+Circle(14) = {9,1,11}; Circle(15) = {10,1,12};
+
+Line Loop(16) = {-6,1,9,10}; Plane Surface(17) = {16};
+Line Loop(18) = {11,12,13,3}; Plane Surface(19) = {18};
+Line Loop(20) = {7,-14,-4,11,12,13,-2,9,10}; Plane Surface(21) = {-20}; // "-" for orientation
+Line Loop(22) = {8,-15,-5,14}; Plane Surface(23) = {-22};
+
+Physical Surface(101) = {21}; /* Air */
+Physical Surface(102) = {17}; /* Core */
+Physical Surface(103) = {19}; /* Ind */
+Physical Surface(111) = {23}; /* AirInf */
+
+Physical Line(1100) = {1,2,3,4,5}; /* Surface ht = 0 */
+Physical Line(1101) = {6,7,8}; /* Surface bn = 0 */
+Physical Line(1102) = {15}; /* Surface Inf */
+
diff --git a/Magnetodynamics/electromagnet.pro b/Magnetodynamics/electromagnet.pro
index 7cf6322..1daf5af 100644
--- a/Magnetodynamics/electromagnet.pro
+++ b/Magnetodynamics/electromagnet.pro
@@ -1,89 +1,89 @@
-/* -------------------------------------------------------------------
- Tutorial 7a : magnetic fields of an electromagnet
-
- Features:
- - Use of a template formulation library
- - Identical to Tutorial 2 for a static current source
- - Frequency-domain solution (phasor) for a dynamic current source
-
- To compute the static solution in a terminal:
- getdp electromagnet -solve MagSta_a_2D -pos Map_a
-
- To compute the time-harmonic dynamic solution in a terminal:
- getdp electromagnet -solve MagDyn_a_2D -pos Map_a
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > electromagnet.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-Include "electromagnet_common.pro";
-
-Group {
- // Physical regions
- Air = Region[ 101 ]; Core = Region[ 102 ];
- Ind = Region[ 103 ]; AirInf = Region[ 111 ];
- Surface_ht0 = Region[ 1100 ];
- Surface_bn0 = Region[ 1101 ];
- Surface_Inf = Region[ 1102 ];
-
- // Abstract regions used in the "Lib_MagStaDyn_av_2D_Cir.pro" template file
- // that is included below:
- VolCC_Mag = Region[{Air, AirInf}]; // Non-conducting regions
- VolC_Mag = Region[{Core}]; // Massive conducting regions
- VolS_Mag = Region[{Ind}]; // Stranded conductors, i.e., coils
- VolInf_Mag = Region[{AirInf}]; // Annulus for infinite shell transformation
- Val_Rint = rInt; Val_Rext = rExt; // Interior and exterior radii of annulus
-}
-
-Function {
- DefineConstant[
- murCore = {100, Name "Model parameters/Mur core"},
- Current = {0.01, Name "Model parameters/Current"}
- ];
-
- mu0 = 4.e-7 * Pi;
- nu[ Region[{Air, Ind, AirInf}] ] = 1. / mu0;
- nu[ Core ] = 1. / (murCore * mu0);
-
- sigma[ Core ] = 1e6 / 10;
- sigma[ Ind ] = 5e7;
-
- Ns[ Ind ] = 1000 ; // number of turns in coil
- Sc[ Ind ] = SurfaceArea[] ; // surface (cross section) of coil
- // Current density in each coil portion for a unit current (will be multiplied
- // by the actual total current in the coil)
- js0[ Ind ] = Ns[]/Sc[] * Vector[0,0,-1];
- CoefGeos[] = 1;
-}
-
-Constraint {
- { Name MagneticVectorPotential_2D;
- Case {
- { Region Surface_bn0; Value 0; }
- { Region Surface_Inf; Value 0; }
- }
- }
- { Name Current_2D;
- Case {
- // represents the phasor amplitude for a dynamic analysis
- { Region Ind; Value Current; }
- }
- }
- { Name Voltage_2D;
- Case {
- { Region Core; Value 0; }
- }
- }
-}
-
-Include "Lib_MagStaDyn_av_2D_Cir.pro";
-
-PostOperation {
- { Name Map_a; NameOfPostProcessing MagDyn_a_2D;
- Operation {
- Print[ a, OnElementsOf Vol_Mag, File "a.pos" ];
- Print[ b, OnElementsOf Vol_Mag, File "b.pos" ];
- }
- }
-}
+/* -------------------------------------------------------------------
+ Tutorial 7a : magnetic fields of an electromagnet
+
+ Features:
+ - Use of a template formulation library
+ - Identical to Tutorial 2 for a static current source
+ - Frequency-domain solution (phasor) for a dynamic current source
+
+ To compute the static solution in a terminal:
+ getdp electromagnet -solve MagSta_a_2D -pos Map_a
+
+ To compute the time-harmonic dynamic solution in a terminal:
+ getdp electromagnet -solve MagDyn_a_2D -pos Map_a
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > electromagnet.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+Include "electromagnet_common.pro";
+
+Group {
+ // Physical regions
+ Air = Region[ 101 ]; Core = Region[ 102 ];
+ Ind = Region[ 103 ]; AirInf = Region[ 111 ];
+ Surface_ht0 = Region[ 1100 ];
+ Surface_bn0 = Region[ 1101 ];
+ Surface_Inf = Region[ 1102 ];
+
+ // Abstract regions used in the "Lib_MagStaDyn_av_2D_Cir.pro" template file
+ // that is included below:
+ VolCC_Mag = Region[{Air, AirInf}]; // Non-conducting regions
+ VolC_Mag = Region[{Core}]; // Massive conducting regions
+ VolS_Mag = Region[{Ind}]; // Stranded conductors, i.e., coils
+ VolInf_Mag = Region[{AirInf}]; // Annulus for infinite shell transformation
+ Val_Rint = rInt; Val_Rext = rExt; // Interior and exterior radii of annulus
+}
+
+Function {
+ DefineConstant[
+ murCore = {100, Name "Model parameters/Mur core"},
+ Current = {0.01, Name "Model parameters/Current"}
+ ];
+
+ mu0 = 4.e-7 * Pi;
+ nu[ Region[{Air, Ind, AirInf}] ] = 1. / mu0;
+ nu[ Core ] = 1. / (murCore * mu0);
+
+ sigma[ Core ] = 1e6 / 10;
+ sigma[ Ind ] = 5e7;
+
+ Ns[ Ind ] = 1000 ; // number of turns in coil
+ Sc[ Ind ] = SurfaceArea[] ; // surface (cross section) of coil
+ // Current density in each coil portion for a unit current (will be multiplied
+ // by the actual total current in the coil)
+ js0[ Ind ] = Ns[]/Sc[] * Vector[0,0,-1];
+ CoefGeos[] = 1;
+}
+
+Constraint {
+ { Name MagneticVectorPotential_2D;
+ Case {
+ { Region Surface_bn0; Value 0; }
+ { Region Surface_Inf; Value 0; }
+ }
+ }
+ { Name Current_2D;
+ Case {
+ // represents the phasor amplitude for a dynamic analysis
+ { Region Ind; Value Current; }
+ }
+ }
+ { Name Voltage_2D;
+ Case {
+ { Region Core; Value 0; }
+ }
+ }
+}
+
+Include "Lib_MagStaDyn_av_2D_Cir.pro";
+
+PostOperation {
+ { Name Map_a; NameOfPostProcessing MagDyn_a_2D;
+ Operation {
+ Print[ a, OnElementsOf Vol_Mag, File "a.pos" ];
+ Print[ b, OnElementsOf Vol_Mag, File "b.pos" ];
+ }
+ }
+}
diff --git a/Magnetodynamics/electromagnet_common.pro b/Magnetodynamics/electromagnet_common.pro
index 56879cd..f0dd285 100644
--- a/Magnetodynamics/electromagnet_common.pro
+++ b/Magnetodynamics/electromagnet_common.pro
@@ -1,4 +1,4 @@
-// Parameters shared by Gmsh and GetDP
-
-rInt = 200.e-3;
-rExt = 250.e-3;
+// Parameters shared by Gmsh and GetDP
+
+rInt = 200.e-3;
+rExt = 250.e-3;
diff --git a/Magnetodynamics/transfo.geo b/Magnetodynamics/transfo.geo
index 072bc9b..6243d4b 100644
--- a/Magnetodynamics/transfo.geo
+++ b/Magnetodynamics/transfo.geo
@@ -1,173 +1,173 @@
-
-Include "transfo_common.pro";
-
-Solver.AutoShowLastStep = 0; // don't automatically show the last time step
-
-// CORE
-
-p_Leg_1_L_0=newp; Point(newp) = {-width_Core/2., 0, 0, c_Core};
-p_Leg_1_R_0=newp; Point(newp) = {-width_Core/2.+width_Core_Leg, 0, 0, c_Core};
-
-p_Leg_1_L_1=newp; Point(newp) = {-width_Core/2., height_Core/2., 0, c_Core};
-p_Leg_1_R_1=newp; Point(newp) = {-width_Core/2.+width_Core_Leg, height_Core/2.-width_Core_Leg, 0, c_Core};
-
-
-p_Leg_2_L_0=newp; Point(newp) = {width_Core/2.-width_Core_Leg, 0, 0, c_Core};
-p_Leg_2_R_0=newp; Point(newp) = {width_Core/2., 0, 0, c_Core};
-
-p_Leg_2_L_1=newp; Point(newp) = {width_Core/2.-width_Core_Leg, height_Core/2.-width_Core_Leg, 0, c_Core};
-p_Leg_2_R_1=newp; Point(newp) = {width_Core/2., height_Core/2., 0, c_Core};
-
-
-l_Core_In[]={};
-l_Core_In[]+=newl; Line(newl) = {p_Leg_1_R_0, p_Leg_1_R_1};
-l_Core_In[]+=newl; Line(newl) = {p_Leg_1_R_1, p_Leg_2_L_1};
-l_Core_In[]+=newl; Line(newl) = {p_Leg_2_L_1, p_Leg_2_L_0};
-
-l_Core_Out[]={};
-l_Core_Out[]+=newl; Line(newl) = {p_Leg_2_R_0, p_Leg_2_R_1};
-l_Core_Out[]+=newl; Line(newl) = {p_Leg_2_R_1, p_Leg_1_L_1};
-l_Core_Out[]+=newl; Line(newl) = {p_Leg_1_L_1, p_Leg_1_L_0};
-
-l_Core_Leg_1_Y0[]={};
-l_Core_Leg_1_Y0[]+=newl; Line(newl) = {p_Leg_1_L_0, p_Leg_1_R_0};
-
-l_Core_Leg_2_Y0[]={};
-l_Core_Leg_2_Y0[]+=newl; Line(newl) = {p_Leg_2_L_0, p_Leg_2_R_0};
-
-
-ll_Core=newll; Line Loop(newll) = {l_Core_In[], l_Core_Leg_2_Y0[], l_Core_Out[], l_Core_Leg_1_Y0[]};
-s_Core=news; Plane Surface(news) = {ll_Core};
-
-Physical Surface("CORE", CORE) = {s_Core};
-
-// COIL_1_PLUS
-
-x_[]=Point{p_Leg_1_R_0};
-p_Coil_1_p_int_0=newp; Point(newp) = {x_[0]+gap_Core_Coil_1, 0, 0, c_Coil_1};
-p_Coil_1_p_ext_0=newp; Point(newp) = {x_[0]+gap_Core_Coil_1+width_Coil_1, 0, 0, c_Coil_1};
-p_Coil_1_p_int_1=newp; Point(newp) = {x_[0]+gap_Core_Coil_1, height_Coil_1/2, 0, c_Coil_1};
-p_Coil_1_p_ext_1=newp; Point(newp) = {x_[0]+gap_Core_Coil_1+width_Coil_1, height_Coil_1/2, 0, c_Coil_1};
-
-l_Coil_1_p[]={};
-l_Coil_1_p[]+=newl; Line(newl) = {p_Coil_1_p_ext_0, p_Coil_1_p_ext_1};
-l_Coil_1_p[]+=newl; Line(newl) = {p_Coil_1_p_ext_1, p_Coil_1_p_int_1};
-l_Coil_1_p[]+=newl; Line(newl) = {p_Coil_1_p_int_1, p_Coil_1_p_int_0};
-
-l_Coil_1_p_Y0[]={};
-l_Coil_1_p_Y0[]+=newl; Line(newl) = {p_Coil_1_p_int_0, p_Coil_1_p_ext_0};
-
-ll_Coil_1_p=newll; Line Loop(newll) = {l_Coil_1_p[], l_Coil_1_p_Y0[]};
-s_Coil_1_p=news; Plane Surface(news) = {ll_Coil_1_p};
-
-Physical Surface("COIL_1_PLUS", COIL_1_PLUS) = {s_Coil_1_p};
-
-
-// COIL_1_MINUS
-
-x_[]=Point{p_Leg_1_L_0};
-p_Coil_1_m_int_0=newp; Point(newp) = {x_[0]-gap_Core_Coil_1, 0, 0, c_Coil_1};
-p_Coil_1_m_ext_0=newp; Point(newp) = {x_[0]-(gap_Core_Coil_1+width_Coil_1), 0, 0, c_Coil_1};
-p_Coil_1_m_int_1=newp; Point(newp) = {x_[0]-gap_Core_Coil_1, height_Coil_1/2, 0, c_Coil_1};
-p_Coil_1_m_ext_1=newp; Point(newp) = {x_[0]-(gap_Core_Coil_1+width_Coil_1), height_Coil_1/2, 0, c_Coil_1};
-
-l_Coil_1_m[]={};
-l_Coil_1_m[]+=newl; Line(newl) = {p_Coil_1_m_ext_0, p_Coil_1_m_ext_1};
-l_Coil_1_m[]+=newl; Line(newl) = {p_Coil_1_m_ext_1, p_Coil_1_m_int_1};
-l_Coil_1_m[]+=newl; Line(newl) = {p_Coil_1_m_int_1, p_Coil_1_m_int_0};
-
-l_Coil_1_m_Y0[]={};
-l_Coil_1_m_Y0[]+=newl; Line(newl) = {p_Coil_1_m_int_0, p_Coil_1_m_ext_0};
-
-ll_Coil_1_m=newll; Line Loop(newll) = {l_Coil_1_m[], l_Coil_1_m_Y0[]};
-s_Coil_1_m=news; Plane Surface(news) = {ll_Coil_1_m};
-
-Physical Surface("COIL_1_MINUS", COIL_1_MINUS) = {s_Coil_1_m};
-
-
-// COIL_2_PLUS
-
-x_[]=Point{p_Leg_2_R_0};
-p_Coil_2_p_int_0=newp; Point(newp) = {x_[0]+gap_Core_Coil_2, 0, 0, c_Coil_2};
-p_Coil_2_p_ext_0=newp; Point(newp) = {x_[0]+gap_Core_Coil_2+width_Coil_2, 0, 0, c_Coil_2};
-p_Coil_2_p_int_1=newp; Point(newp) = {x_[0]+gap_Core_Coil_2, height_Coil_2/2, 0, c_Coil_2};
-p_Coil_2_p_ext_1=newp; Point(newp) = {x_[0]+gap_Core_Coil_2+width_Coil_2, height_Coil_2/2, 0, c_Coil_2};
-
-l_Coil_2_p[]={};
-l_Coil_2_p[]+=newl; Line(newl) = {p_Coil_2_p_ext_0, p_Coil_2_p_ext_1};
-l_Coil_2_p[]+=newl; Line(newl) = {p_Coil_2_p_ext_1, p_Coil_2_p_int_1};
-l_Coil_2_p[]+=newl; Line(newl) = {p_Coil_2_p_int_1, p_Coil_2_p_int_0};
-
-l_Coil_2_p_Y0[]={};
-l_Coil_2_p_Y0[]+=newl; Line(newl) = {p_Coil_2_p_int_0, p_Coil_2_p_ext_0};
-
-ll_Coil_2_p=newll; Line Loop(newll) = {l_Coil_2_p[], l_Coil_2_p_Y0[]};
-s_Coil_2_p=news; Plane Surface(news) = {ll_Coil_2_p};
-
-Physical Surface("COIL_2_PLUS", COIL_2_PLUS) = {s_Coil_2_p};
-
-
-// COIL_2_MINUS
-
-x_[]=Point{p_Leg_2_L_0};
-p_Coil_2_m_int_0=newp; Point(newp) = {x_[0]-gap_Core_Coil_2, 0, 0, c_Coil_2};
-p_Coil_2_m_ext_0=newp; Point(newp) = {x_[0]-(gap_Core_Coil_2+width_Coil_2), 0, 0, c_Coil_2};
-p_Coil_2_m_int_1=newp; Point(newp) = {x_[0]-gap_Core_Coil_2, height_Coil_2/2, 0, c_Coil_2};
-p_Coil_2_m_ext_1=newp; Point(newp) = {x_[0]-(gap_Core_Coil_2+width_Coil_2), height_Coil_2/2, 0, c_Coil_2};
-
-l_Coil_2_m[]={};
-l_Coil_2_m[]+=newl; Line(newl) = {p_Coil_2_m_ext_0, p_Coil_2_m_ext_1};
-l_Coil_2_m[]+=newl; Line(newl) = {p_Coil_2_m_ext_1, p_Coil_2_m_int_1};
-l_Coil_2_m[]+=newl; Line(newl) = {p_Coil_2_m_int_1, p_Coil_2_m_int_0};
-
-l_Coil_2_m_Y0[]={};
-l_Coil_2_m_Y0[]+=newl; Line(newl) = {p_Coil_2_m_int_0, p_Coil_2_m_ext_0};
-
-ll_Coil_2_m=newll; Line Loop(newll) = {l_Coil_2_m[], l_Coil_2_m_Y0[]};
-s_Coil_2_m=news; Plane Surface(news) = {ll_Coil_2_m};
-
-Physical Surface("COIL_2_MINUS", COIL_2_MINUS) = {s_Coil_2_m};
-
-
-// AIR_WINDOW
-
-l_Air_Window_Y0[]={};
-l_Air_Window_Y0[]+=newl; Line(newl) = {p_Leg_1_R_0, p_Coil_1_p_int_0};
-l_Air_Window_Y0[]+=newl; Line(newl) = {p_Coil_1_p_ext_0, p_Coil_2_m_ext_0};
-l_Air_Window_Y0[]+=newl; Line(newl) = {p_Coil_2_m_int_0, p_Leg_2_L_0};
-
-ll_Air_Window=newll; Line Loop(newll) = {-l_Core_In[], -l_Coil_1_p[], l_Coil_2_m[], l_Air_Window_Y0[]};
-s_Air_Window=news; Plane Surface(news) = {ll_Air_Window};
-
-Physical Surface("AIR_WINDOW", AIR_WINDOW) = {s_Air_Window};
-
-
-// AIR_EXT
-
-x_[]=Point{p_Leg_2_R_1};
-p_Air_Ext_1_R_0=newp; Point(newp) = {x_[0]+gap_Core_Box_X, 0, 0, c_Box};
-p_Air_Ext_1_R_1=newp; Point(newp) = {x_[0]+gap_Core_Box_X, x_[1]+gap_Core_Box_Y, 0, c_Box};
-
-x_[]=Point{p_Leg_1_L_1};
-p_Air_Ext_1_L_0=newp; Point(newp) = {x_[0]-gap_Core_Box_X, 0, 0, c_Box};
-p_Air_Ext_1_L_1=newp; Point(newp) = {x_[0]-gap_Core_Box_X, x_[1]+gap_Core_Box_Y, 0, c_Box};
-
-l_Air_Ext[]={};
-l_Air_Ext[]+=newl; Line(newl) = {p_Air_Ext_1_R_0, p_Air_Ext_1_R_1};
-l_Air_Ext[]+=newl; Line(newl) = {p_Air_Ext_1_R_1, p_Air_Ext_1_L_1};
-l_Air_Ext[]+=newl; Line(newl) = {p_Air_Ext_1_L_1, p_Air_Ext_1_L_0};
-
-
-l_Air_Ext_Y0[]={};
-l_Air_Ext_Y0[]+=newl; Line(newl) = {p_Leg_2_R_0, p_Coil_2_p_int_0};
-l_Air_Ext_Y0[]+=newl; Line(newl) = {p_Coil_2_p_ext_0, p_Air_Ext_1_R_0};
-
-l_Air_Ext_Y0[]+=newl; Line(newl) = {p_Air_Ext_1_L_0, p_Coil_1_m_ext_0};
-l_Air_Ext_Y0[]+=newl; Line(newl) = {p_Coil_1_m_int_0, p_Leg_1_L_0};
-
-
-ll_Air_Ext=newll; Line Loop(newll) = {-l_Core_Out[], -l_Coil_2_p[], l_Coil_1_m[], l_Air_Ext[], l_Air_Ext_Y0[]};
-s_Air_Ext=news; Plane Surface(news) = {ll_Air_Ext};
-
-Physical Surface("AIR_EXT", AIR_EXT) = {s_Air_Ext};
-Physical Line("SUR_AIR_EXT", SUR_AIR_EXT) = {l_Air_Ext[]};
+
+Include "transfo_common.pro";
+
+Solver.AutoShowLastStep = 0; // don't automatically show the last time step
+
+// CORE
+
+p_Leg_1_L_0=newp; Point(newp) = {-width_Core/2., 0, 0, c_Core};
+p_Leg_1_R_0=newp; Point(newp) = {-width_Core/2.+width_Core_Leg, 0, 0, c_Core};
+
+p_Leg_1_L_1=newp; Point(newp) = {-width_Core/2., height_Core/2., 0, c_Core};
+p_Leg_1_R_1=newp; Point(newp) = {-width_Core/2.+width_Core_Leg, height_Core/2.-width_Core_Leg, 0, c_Core};
+
+
+p_Leg_2_L_0=newp; Point(newp) = {width_Core/2.-width_Core_Leg, 0, 0, c_Core};
+p_Leg_2_R_0=newp; Point(newp) = {width_Core/2., 0, 0, c_Core};
+
+p_Leg_2_L_1=newp; Point(newp) = {width_Core/2.-width_Core_Leg, height_Core/2.-width_Core_Leg, 0, c_Core};
+p_Leg_2_R_1=newp; Point(newp) = {width_Core/2., height_Core/2., 0, c_Core};
+
+
+l_Core_In[]={};
+l_Core_In[]+=newl; Line(newl) = {p_Leg_1_R_0, p_Leg_1_R_1};
+l_Core_In[]+=newl; Line(newl) = {p_Leg_1_R_1, p_Leg_2_L_1};
+l_Core_In[]+=newl; Line(newl) = {p_Leg_2_L_1, p_Leg_2_L_0};
+
+l_Core_Out[]={};
+l_Core_Out[]+=newl; Line(newl) = {p_Leg_2_R_0, p_Leg_2_R_1};
+l_Core_Out[]+=newl; Line(newl) = {p_Leg_2_R_1, p_Leg_1_L_1};
+l_Core_Out[]+=newl; Line(newl) = {p_Leg_1_L_1, p_Leg_1_L_0};
+
+l_Core_Leg_1_Y0[]={};
+l_Core_Leg_1_Y0[]+=newl; Line(newl) = {p_Leg_1_L_0, p_Leg_1_R_0};
+
+l_Core_Leg_2_Y0[]={};
+l_Core_Leg_2_Y0[]+=newl; Line(newl) = {p_Leg_2_L_0, p_Leg_2_R_0};
+
+
+ll_Core=newll; Line Loop(newll) = {l_Core_In[], l_Core_Leg_2_Y0[], l_Core_Out[], l_Core_Leg_1_Y0[]};
+s_Core=news; Plane Surface(news) = {ll_Core};
+
+Physical Surface("CORE", CORE) = {s_Core};
+
+// COIL_1_PLUS
+
+x_[]=Point{p_Leg_1_R_0};
+p_Coil_1_p_int_0=newp; Point(newp) = {x_[0]+gap_Core_Coil_1, 0, 0, c_Coil_1};
+p_Coil_1_p_ext_0=newp; Point(newp) = {x_[0]+gap_Core_Coil_1+width_Coil_1, 0, 0, c_Coil_1};
+p_Coil_1_p_int_1=newp; Point(newp) = {x_[0]+gap_Core_Coil_1, height_Coil_1/2, 0, c_Coil_1};
+p_Coil_1_p_ext_1=newp; Point(newp) = {x_[0]+gap_Core_Coil_1+width_Coil_1, height_Coil_1/2, 0, c_Coil_1};
+
+l_Coil_1_p[]={};
+l_Coil_1_p[]+=newl; Line(newl) = {p_Coil_1_p_ext_0, p_Coil_1_p_ext_1};
+l_Coil_1_p[]+=newl; Line(newl) = {p_Coil_1_p_ext_1, p_Coil_1_p_int_1};
+l_Coil_1_p[]+=newl; Line(newl) = {p_Coil_1_p_int_1, p_Coil_1_p_int_0};
+
+l_Coil_1_p_Y0[]={};
+l_Coil_1_p_Y0[]+=newl; Line(newl) = {p_Coil_1_p_int_0, p_Coil_1_p_ext_0};
+
+ll_Coil_1_p=newll; Line Loop(newll) = {l_Coil_1_p[], l_Coil_1_p_Y0[]};
+s_Coil_1_p=news; Plane Surface(news) = {ll_Coil_1_p};
+
+Physical Surface("COIL_1_PLUS", COIL_1_PLUS) = {s_Coil_1_p};
+
+
+// COIL_1_MINUS
+
+x_[]=Point{p_Leg_1_L_0};
+p_Coil_1_m_int_0=newp; Point(newp) = {x_[0]-gap_Core_Coil_1, 0, 0, c_Coil_1};
+p_Coil_1_m_ext_0=newp; Point(newp) = {x_[0]-(gap_Core_Coil_1+width_Coil_1), 0, 0, c_Coil_1};
+p_Coil_1_m_int_1=newp; Point(newp) = {x_[0]-gap_Core_Coil_1, height_Coil_1/2, 0, c_Coil_1};
+p_Coil_1_m_ext_1=newp; Point(newp) = {x_[0]-(gap_Core_Coil_1+width_Coil_1), height_Coil_1/2, 0, c_Coil_1};
+
+l_Coil_1_m[]={};
+l_Coil_1_m[]+=newl; Line(newl) = {p_Coil_1_m_ext_0, p_Coil_1_m_ext_1};
+l_Coil_1_m[]+=newl; Line(newl) = {p_Coil_1_m_ext_1, p_Coil_1_m_int_1};
+l_Coil_1_m[]+=newl; Line(newl) = {p_Coil_1_m_int_1, p_Coil_1_m_int_0};
+
+l_Coil_1_m_Y0[]={};
+l_Coil_1_m_Y0[]+=newl; Line(newl) = {p_Coil_1_m_int_0, p_Coil_1_m_ext_0};
+
+ll_Coil_1_m=newll; Line Loop(newll) = {l_Coil_1_m[], l_Coil_1_m_Y0[]};
+s_Coil_1_m=news; Plane Surface(news) = {ll_Coil_1_m};
+
+Physical Surface("COIL_1_MINUS", COIL_1_MINUS) = {s_Coil_1_m};
+
+
+// COIL_2_PLUS
+
+x_[]=Point{p_Leg_2_R_0};
+p_Coil_2_p_int_0=newp; Point(newp) = {x_[0]+gap_Core_Coil_2, 0, 0, c_Coil_2};
+p_Coil_2_p_ext_0=newp; Point(newp) = {x_[0]+gap_Core_Coil_2+width_Coil_2, 0, 0, c_Coil_2};
+p_Coil_2_p_int_1=newp; Point(newp) = {x_[0]+gap_Core_Coil_2, height_Coil_2/2, 0, c_Coil_2};
+p_Coil_2_p_ext_1=newp; Point(newp) = {x_[0]+gap_Core_Coil_2+width_Coil_2, height_Coil_2/2, 0, c_Coil_2};
+
+l_Coil_2_p[]={};
+l_Coil_2_p[]+=newl; Line(newl) = {p_Coil_2_p_ext_0, p_Coil_2_p_ext_1};
+l_Coil_2_p[]+=newl; Line(newl) = {p_Coil_2_p_ext_1, p_Coil_2_p_int_1};
+l_Coil_2_p[]+=newl; Line(newl) = {p_Coil_2_p_int_1, p_Coil_2_p_int_0};
+
+l_Coil_2_p_Y0[]={};
+l_Coil_2_p_Y0[]+=newl; Line(newl) = {p_Coil_2_p_int_0, p_Coil_2_p_ext_0};
+
+ll_Coil_2_p=newll; Line Loop(newll) = {l_Coil_2_p[], l_Coil_2_p_Y0[]};
+s_Coil_2_p=news; Plane Surface(news) = {ll_Coil_2_p};
+
+Physical Surface("COIL_2_PLUS", COIL_2_PLUS) = {s_Coil_2_p};
+
+
+// COIL_2_MINUS
+
+x_[]=Point{p_Leg_2_L_0};
+p_Coil_2_m_int_0=newp; Point(newp) = {x_[0]-gap_Core_Coil_2, 0, 0, c_Coil_2};
+p_Coil_2_m_ext_0=newp; Point(newp) = {x_[0]-(gap_Core_Coil_2+width_Coil_2), 0, 0, c_Coil_2};
+p_Coil_2_m_int_1=newp; Point(newp) = {x_[0]-gap_Core_Coil_2, height_Coil_2/2, 0, c_Coil_2};
+p_Coil_2_m_ext_1=newp; Point(newp) = {x_[0]-(gap_Core_Coil_2+width_Coil_2), height_Coil_2/2, 0, c_Coil_2};
+
+l_Coil_2_m[]={};
+l_Coil_2_m[]+=newl; Line(newl) = {p_Coil_2_m_ext_0, p_Coil_2_m_ext_1};
+l_Coil_2_m[]+=newl; Line(newl) = {p_Coil_2_m_ext_1, p_Coil_2_m_int_1};
+l_Coil_2_m[]+=newl; Line(newl) = {p_Coil_2_m_int_1, p_Coil_2_m_int_0};
+
+l_Coil_2_m_Y0[]={};
+l_Coil_2_m_Y0[]+=newl; Line(newl) = {p_Coil_2_m_int_0, p_Coil_2_m_ext_0};
+
+ll_Coil_2_m=newll; Line Loop(newll) = {l_Coil_2_m[], l_Coil_2_m_Y0[]};
+s_Coil_2_m=news; Plane Surface(news) = {ll_Coil_2_m};
+
+Physical Surface("COIL_2_MINUS", COIL_2_MINUS) = {s_Coil_2_m};
+
+
+// AIR_WINDOW
+
+l_Air_Window_Y0[]={};
+l_Air_Window_Y0[]+=newl; Line(newl) = {p_Leg_1_R_0, p_Coil_1_p_int_0};
+l_Air_Window_Y0[]+=newl; Line(newl) = {p_Coil_1_p_ext_0, p_Coil_2_m_ext_0};
+l_Air_Window_Y0[]+=newl; Line(newl) = {p_Coil_2_m_int_0, p_Leg_2_L_0};
+
+ll_Air_Window=newll; Line Loop(newll) = {-l_Core_In[], -l_Coil_1_p[], l_Coil_2_m[], l_Air_Window_Y0[]};
+s_Air_Window=news; Plane Surface(news) = {ll_Air_Window};
+
+Physical Surface("AIR_WINDOW", AIR_WINDOW) = {s_Air_Window};
+
+
+// AIR_EXT
+
+x_[]=Point{p_Leg_2_R_1};
+p_Air_Ext_1_R_0=newp; Point(newp) = {x_[0]+gap_Core_Box_X, 0, 0, c_Box};
+p_Air_Ext_1_R_1=newp; Point(newp) = {x_[0]+gap_Core_Box_X, x_[1]+gap_Core_Box_Y, 0, c_Box};
+
+x_[]=Point{p_Leg_1_L_1};
+p_Air_Ext_1_L_0=newp; Point(newp) = {x_[0]-gap_Core_Box_X, 0, 0, c_Box};
+p_Air_Ext_1_L_1=newp; Point(newp) = {x_[0]-gap_Core_Box_X, x_[1]+gap_Core_Box_Y, 0, c_Box};
+
+l_Air_Ext[]={};
+l_Air_Ext[]+=newl; Line(newl) = {p_Air_Ext_1_R_0, p_Air_Ext_1_R_1};
+l_Air_Ext[]+=newl; Line(newl) = {p_Air_Ext_1_R_1, p_Air_Ext_1_L_1};
+l_Air_Ext[]+=newl; Line(newl) = {p_Air_Ext_1_L_1, p_Air_Ext_1_L_0};
+
+
+l_Air_Ext_Y0[]={};
+l_Air_Ext_Y0[]+=newl; Line(newl) = {p_Leg_2_R_0, p_Coil_2_p_int_0};
+l_Air_Ext_Y0[]+=newl; Line(newl) = {p_Coil_2_p_ext_0, p_Air_Ext_1_R_0};
+
+l_Air_Ext_Y0[]+=newl; Line(newl) = {p_Air_Ext_1_L_0, p_Coil_1_m_ext_0};
+l_Air_Ext_Y0[]+=newl; Line(newl) = {p_Coil_1_m_int_0, p_Leg_1_L_0};
+
+
+ll_Air_Ext=newll; Line Loop(newll) = {-l_Core_Out[], -l_Coil_2_p[], l_Coil_1_m[], l_Air_Ext[], l_Air_Ext_Y0[]};
+s_Air_Ext=news; Plane Surface(news) = {ll_Air_Ext};
+
+Physical Surface("AIR_EXT", AIR_EXT) = {s_Air_Ext};
+Physical Line("SUR_AIR_EXT", SUR_AIR_EXT) = {l_Air_Ext[]};
diff --git a/Magnetodynamics/transfo.pro b/Magnetodynamics/transfo.pro
index b3b1ece..88f0dba 100644
--- a/Magnetodynamics/transfo.pro
+++ b/Magnetodynamics/transfo.pro
@@ -1,259 +1,259 @@
-/* -------------------------------------------------------------------
- Tutorial 7b : magnetodyamic model of a single-phase transformer
-
- Features:
- - Use of a generic template formulation library
- - Frequency- and time-domain dynamic solutions
- - Circuit coupling used as a black-box (see Tutorial 8 for details)
-
- To compute the solution in a terminal:
- getdp transfo -solve MagDyn_a_2D -pos Map_a
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > transfo.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-Include "transfo_common.pro";
-
-DefineConstant[
- type_Conds = {2, Choices{1 = "Massive", 2 = "Coil"}, Highlight "Blue",
- Name "Parameters/01Conductor type"}
- type_Source = {2, Choices{1 = "Current", 2 = "Voltage"}, Highlight "Blue",
- Name "Parameters/02Source type"}
- type_Analysis = {1, Choices{1 = "Frequency-domain", 2 = "Time-domain"}, Highlight "Blue",
- Name "Parameters/03Analysis type"}
- Freq = {50, Min 0, Max 1e3, Step 1,
- Name "Parameters/Frequency"}
-];
-
-Group {
- /* Abstract regions that will be used in the "Lib_MagStaDyn_av_2D_Cir.pro"
- template file included below; the regions are first intialized as empty,
- before being filled with physical groups */
-
- VolCC_Mag = Region[{}]; // Non-conducting regions
- VolC_Mag = Region[{}]; // Massive conductors
- VolS_Mag = Region[{}]; // Stranded conductors, i.e., coils
-
- // air physical groups
- Air = Region[{AIR_WINDOW, AIR_EXT}];
- VolCC_Mag += Region[Air];
-
- // exterior boundary
- Sur_Air_Ext = Region[{SUR_AIR_EXT}];
-
- // magnetic core of the transformer, assumed to be non-conducting
- Core = Region[CORE];
- VolCC_Mag += Region[Core];
-
- Coil_1_P = Region[COIL_1_PLUS];
- Coil_1_M = Region[COIL_1_MINUS];
- Coil_1 = Region[{Coil_1_P, Coil_1_M}];
-
- Coil_2_P = Region[COIL_2_PLUS];
- Coil_2_M = Region[COIL_2_MINUS];
- Coil_2 = Region[{Coil_2_P, Coil_2_M}];
-
- Coils = Region[{Coil_1, Coil_2}];
-
- If (type_Conds == 1)
- VolC_Mag += Region[{Coils}];
- ElseIf (type_Conds == 2)
- VolS_Mag += Region[{Coils}];
- VolCC_Mag += Region[{Coils}];
- EndIf
-}
-
-
-Function {
- mu0 = 4e-7*Pi;
-
- mu[Air] = 1 * mu0;
-
- mur_Core = 100;
- mu[Core] = mur_Core * mu0;
-
- mu[Coils] = 1 * mu0;
- sigma[Coils] = 1e7;
-
- // For a correct definition of the voltage
- CoefGeo = thickness_Core;
-
- // To be defined separately for each coil portion
- Sc[Coil_1_P] = SurfaceArea[];
- SignBranch[Coil_1_P] = 1; // To fix the convention of positive current (1:
- // along Oz, -1: along -Oz)
-
- Sc[Coil_1_M] = SurfaceArea[];
- SignBranch[Coil_1_M] = -1;
-
- Sc[Coil_2_P] = SurfaceArea[];
- SignBranch[Coil_2_P] = 1;
-
- Sc[Coil_2_M] = SurfaceArea[];
- SignBranch[Coil_2_M] = -1;
-
- // Number of turns (same for PLUS and MINUS portions) (half values because
- // half coils are defined)
- Ns[Coil_1] = 1;
- Ns[Coil_2] = 1;
-
- // Global definitions (nothing to change):
-
- // Current density in each coil portion for a unit current (will be multiplied
- // by the actual total current in the coil)
- js0[Coils] = Ns[]/Sc[] * Vector[0,0,SignBranch[]];
- CoefGeos[Coils] = SignBranch[] * CoefGeo;
-
- // The reluctivity will be used
- nu[] = 1/mu[];
-}
-
-If(type_Analysis == 1)
- Flag_FrequencyDomain = 1;
-Else
- Flag_FrequencyDomain = 0;
-EndIf
-
-If (type_Source == 1) // current
-
- Flag_CircuitCoupling = 0;
-
-ElseIf (type_Source == 2) // voltage
-
- // PLUS and MINUS coil portions to be connected in series, with applied
- // voltage on the resulting branch
- Flag_CircuitCoupling = 1;
-
- // Here is the definition of the circuits on primary and secondary sides:
- Group {
- // Empty Groups to be filled
- Resistance_Cir = Region[{}];
- Inductance_Cir = Region[{}] ;
- Capacitance_Cir = Region[{}] ;
- SourceV_Cir = Region[{}]; // Voltage sources
- SourceI_Cir = Region[{}]; // Current sources
-
- // Primary side
- E_in = Region[10001]; // arbitrary region number (not linked to the mesh)
- SourceV_Cir += Region[{E_in}];
-
- // Secondary side
- R_out = Region[10101]; // arbitrary region number (not linked to the mesh)
- Resistance_Cir += Region[{R_out}];
- }
-
- Function {
- deg = Pi/180;
- // Input RMS voltage (half of the voltage because of symmetry; half coils
- // are defined)
- val_E_in = 1.;
- phase_E_in = 90 *deg; // Phase in radian (from phase in degree)
- // High value for an open-circuit test; Low value for a short-circuit test;
- // any value in-between for any charge
- Resistance[R_out] = 1e6;
- }
-
- Constraint {
-
- { Name Current_Cir ;
- Case {
- }
- }
-
- { Name Voltage_Cir ;
- Case {
- { Region E_in; Value val_E_in; TimeFunction F_Cos_wt_p[]{2*Pi*Freq, phase_E_in}; }
- }
- }
-
- { Name ElectricalCircuit ; Type Network ;
- Case Circuit_1 {
- // PLUS and MINUS coil portions to be connected in series, together with
- // E_in (an additional resistor should be defined to represent the
- // Coil_1 end-winding (not considered in the 2D model))
- { Region E_in; Branch {1,2}; }
-
- { Region Coil_1_P; Branch {2,3} ; }
- { Region Coil_1_M; Branch {3,1} ; }
- }
- Case Circuit_2 {
- // PLUS and MINUS coil portions to be connected in series, together with
- // R_out (an additional resistor should be defined to represent the
- // Coil_2 end-winding (not considered in the 2D model))
- { Region R_out; Branch {1,2}; }
-
- { Region Coil_2_P; Branch {2,3} ; }
- { Region Coil_2_M; Branch {3,1} ; }
- }
- }
-
- }
-
-EndIf
-
-Constraint {
- { Name MagneticVectorPotential_2D;
- Case {
- { Region Sur_Air_Ext; Value 0; }
- }
- }
- { Name Current_2D;
- Case {
- If (type_Source == 1)
- // Current in each coil (same for PLUS and MINUS portions)
- { Region Coil_1; Value 1; TimeFunction F_Sin_wt_p[]{2*Pi*Freq, 0}; }
- { Region Coil_2; Value 0; }
- EndIf
- }
- }
- { Name Voltage_2D;
- Case {
- }
- }
-}
-
-Include "Lib_MagStaDyn_av_2D_Cir.pro";
-
-PostOperation {
- { Name Map_a; NameOfPostProcessing MagDyn_a_2D;
- Operation {
- Print[ j, OnElementsOf Region[{VolC_Mag, VolS_Mag}], Format Gmsh, File "j.pos" ];
- Print[ b, OnElementsOf Vol_Mag, Format Gmsh, File "b.pos" ];
- Print[ az, OnElementsOf Vol_Mag, Format Gmsh, File "az.pos" ];
-
- If (type_Source == 1) // current
- // In text file UI.txt: voltage and current for each coil portion (note
- // that the voltage is not equally distributed in PLUS and MINUS
- // portions, which is the reason why we must apply the total voltage
- // through a circuit -> type_Source == 2)
- Echo[ "Coil_1_P", Format Table, File "UI.txt" ];
- Print[ U, OnRegion Coil_1_P, Format FrequencyTable, File > "UI.txt" ];
- Print[ I, OnRegion Coil_1_P, Format FrequencyTable, File > "UI.txt"];
- Echo[ "Coil_1_M", Format Table, File > "UI.txt" ];
- Print[ U, OnRegion Coil_1_M, Format FrequencyTable, File > "UI.txt" ];
- Print[ I, OnRegion Coil_1_M, Format FrequencyTable, File > "UI.txt"];
-
- Echo[ "Coil_2_P", Format Table, File > "UI.txt" ];
- Print[ U, OnRegion Coil_2_P, Format FrequencyTable, File > "UI.txt" ];
- Print[ I, OnRegion Coil_2_P, Format FrequencyTable, File > "UI.txt"];
- Echo[ "Coil_2_M", Format Table, File > "UI.txt" ];
- Print[ U, OnRegion Coil_2_M, Format FrequencyTable, File > "UI.txt" ];
- Print[ I, OnRegion Coil_2_M, Format FrequencyTable, File > "UI.txt"];
-
- ElseIf (type_Source == 2)
- // In text file UI.txt: voltage and current of the primary coil (from E_in)
- // (real and imaginary parts!)
- Echo[ "E_in", Format Table, File "UI.txt" ];
- Print[ U, OnRegion E_in, Format FrequencyTable, File > "UI.txt" ];
- Print[ I, OnRegion E_in, Format FrequencyTable, File > "UI.txt"];
-
- // In text file UI.txt: voltage and current of the secondary coil (from R_out)
- Echo[ "R_out", Format Table, File > "UI.txt" ];
- Print[ U, OnRegion R_out, Format FrequencyTable, File > "UI.txt" ];
- Print[ I, OnRegion R_out, Format FrequencyTable, File > "UI.txt"];
- EndIf
- }
- }
-}
+/* -------------------------------------------------------------------
+ Tutorial 7b : magnetodyamic model of a single-phase transformer
+
+ Features:
+ - Use of a generic template formulation library
+ - Frequency- and time-domain dynamic solutions
+ - Circuit coupling used as a black-box (see Tutorial 8 for details)
+
+ To compute the solution in a terminal:
+ getdp transfo -solve MagDyn_a_2D -pos Map_a
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > transfo.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+Include "transfo_common.pro";
+
+DefineConstant[
+ type_Conds = {2, Choices{1 = "Massive", 2 = "Coil"}, Highlight "Blue",
+ Name "Parameters/01Conductor type"}
+ type_Source = {2, Choices{1 = "Current", 2 = "Voltage"}, Highlight "Blue",
+ Name "Parameters/02Source type"}
+ type_Analysis = {1, Choices{1 = "Frequency-domain", 2 = "Time-domain"}, Highlight "Blue",
+ Name "Parameters/03Analysis type"}
+ Freq = {50, Min 0, Max 1e3, Step 1,
+ Name "Parameters/Frequency"}
+];
+
+Group {
+ /* Abstract regions that will be used in the "Lib_MagStaDyn_av_2D_Cir.pro"
+ template file included below; the regions are first intialized as empty,
+ before being filled with physical groups */
+
+ VolCC_Mag = Region[{}]; // Non-conducting regions
+ VolC_Mag = Region[{}]; // Massive conductors
+ VolS_Mag = Region[{}]; // Stranded conductors, i.e., coils
+
+ // air physical groups
+ Air = Region[{AIR_WINDOW, AIR_EXT}];
+ VolCC_Mag += Region[Air];
+
+ // exterior boundary
+ Sur_Air_Ext = Region[{SUR_AIR_EXT}];
+
+ // magnetic core of the transformer, assumed to be non-conducting
+ Core = Region[CORE];
+ VolCC_Mag += Region[Core];
+
+ Coil_1_P = Region[COIL_1_PLUS];
+ Coil_1_M = Region[COIL_1_MINUS];
+ Coil_1 = Region[{Coil_1_P, Coil_1_M}];
+
+ Coil_2_P = Region[COIL_2_PLUS];
+ Coil_2_M = Region[COIL_2_MINUS];
+ Coil_2 = Region[{Coil_2_P, Coil_2_M}];
+
+ Coils = Region[{Coil_1, Coil_2}];
+
+ If (type_Conds == 1)
+ VolC_Mag += Region[{Coils}];
+ ElseIf (type_Conds == 2)
+ VolS_Mag += Region[{Coils}];
+ VolCC_Mag += Region[{Coils}];
+ EndIf
+}
+
+
+Function {
+ mu0 = 4e-7*Pi;
+
+ mu[Air] = 1 * mu0;
+
+ mur_Core = 100;
+ mu[Core] = mur_Core * mu0;
+
+ mu[Coils] = 1 * mu0;
+ sigma[Coils] = 1e7;
+
+ // For a correct definition of the voltage
+ CoefGeo = thickness_Core;
+
+ // To be defined separately for each coil portion
+ Sc[Coil_1_P] = SurfaceArea[];
+ SignBranch[Coil_1_P] = 1; // To fix the convention of positive current (1:
+ // along Oz, -1: along -Oz)
+
+ Sc[Coil_1_M] = SurfaceArea[];
+ SignBranch[Coil_1_M] = -1;
+
+ Sc[Coil_2_P] = SurfaceArea[];
+ SignBranch[Coil_2_P] = 1;
+
+ Sc[Coil_2_M] = SurfaceArea[];
+ SignBranch[Coil_2_M] = -1;
+
+ // Number of turns (same for PLUS and MINUS portions) (half values because
+ // half coils are defined)
+ Ns[Coil_1] = 1;
+ Ns[Coil_2] = 1;
+
+ // Global definitions (nothing to change):
+
+ // Current density in each coil portion for a unit current (will be multiplied
+ // by the actual total current in the coil)
+ js0[Coils] = Ns[]/Sc[] * Vector[0,0,SignBranch[]];
+ CoefGeos[Coils] = SignBranch[] * CoefGeo;
+
+ // The reluctivity will be used
+ nu[] = 1/mu[];
+}
+
+If(type_Analysis == 1)
+ Flag_FrequencyDomain = 1;
+Else
+ Flag_FrequencyDomain = 0;
+EndIf
+
+If (type_Source == 1) // current
+
+ Flag_CircuitCoupling = 0;
+
+ElseIf (type_Source == 2) // voltage
+
+ // PLUS and MINUS coil portions to be connected in series, with applied
+ // voltage on the resulting branch
+ Flag_CircuitCoupling = 1;
+
+ // Here is the definition of the circuits on primary and secondary sides:
+ Group {
+ // Empty Groups to be filled
+ Resistance_Cir = Region[{}];
+ Inductance_Cir = Region[{}] ;
+ Capacitance_Cir = Region[{}] ;
+ SourceV_Cir = Region[{}]; // Voltage sources
+ SourceI_Cir = Region[{}]; // Current sources
+
+ // Primary side
+ E_in = Region[10001]; // arbitrary region number (not linked to the mesh)
+ SourceV_Cir += Region[{E_in}];
+
+ // Secondary side
+ R_out = Region[10101]; // arbitrary region number (not linked to the mesh)
+ Resistance_Cir += Region[{R_out}];
+ }
+
+ Function {
+ deg = Pi/180;
+ // Input RMS voltage (half of the voltage because of symmetry; half coils
+ // are defined)
+ val_E_in = 1.;
+ phase_E_in = 90 *deg; // Phase in radian (from phase in degree)
+ // High value for an open-circuit test; Low value for a short-circuit test;
+ // any value in-between for any charge
+ Resistance[R_out] = 1e6;
+ }
+
+ Constraint {
+
+ { Name Current_Cir ;
+ Case {
+ }
+ }
+
+ { Name Voltage_Cir ;
+ Case {
+ { Region E_in; Value val_E_in; TimeFunction F_Cos_wt_p[]{2*Pi*Freq, phase_E_in}; }
+ }
+ }
+
+ { Name ElectricalCircuit ; Type Network ;
+ Case Circuit_1 {
+ // PLUS and MINUS coil portions to be connected in series, together with
+ // E_in (an additional resistor should be defined to represent the
+ // Coil_1 end-winding (not considered in the 2D model))
+ { Region E_in; Branch {1,2}; }
+
+ { Region Coil_1_P; Branch {2,3} ; }
+ { Region Coil_1_M; Branch {3,1} ; }
+ }
+ Case Circuit_2 {
+ // PLUS and MINUS coil portions to be connected in series, together with
+ // R_out (an additional resistor should be defined to represent the
+ // Coil_2 end-winding (not considered in the 2D model))
+ { Region R_out; Branch {1,2}; }
+
+ { Region Coil_2_P; Branch {2,3} ; }
+ { Region Coil_2_M; Branch {3,1} ; }
+ }
+ }
+
+ }
+
+EndIf
+
+Constraint {
+ { Name MagneticVectorPotential_2D;
+ Case {
+ { Region Sur_Air_Ext; Value 0; }
+ }
+ }
+ { Name Current_2D;
+ Case {
+ If (type_Source == 1)
+ // Current in each coil (same for PLUS and MINUS portions)
+ { Region Coil_1; Value 1; TimeFunction F_Sin_wt_p[]{2*Pi*Freq, 0}; }
+ { Region Coil_2; Value 0; }
+ EndIf
+ }
+ }
+ { Name Voltage_2D;
+ Case {
+ }
+ }
+}
+
+Include "Lib_MagStaDyn_av_2D_Cir.pro";
+
+PostOperation {
+ { Name Map_a; NameOfPostProcessing MagDyn_a_2D;
+ Operation {
+ Print[ j, OnElementsOf Region[{VolC_Mag, VolS_Mag}], Format Gmsh, File "j.pos" ];
+ Print[ b, OnElementsOf Vol_Mag, Format Gmsh, File "b.pos" ];
+ Print[ az, OnElementsOf Vol_Mag, Format Gmsh, File "az.pos" ];
+
+ If (type_Source == 1) // current
+ // In text file UI.txt: voltage and current for each coil portion (note
+ // that the voltage is not equally distributed in PLUS and MINUS
+ // portions, which is the reason why we must apply the total voltage
+ // through a circuit -> type_Source == 2)
+ Echo[ "Coil_1_P", Format Table, File "UI.txt" ];
+ Print[ U, OnRegion Coil_1_P, Format FrequencyTable, File > "UI.txt" ];
+ Print[ I, OnRegion Coil_1_P, Format FrequencyTable, File > "UI.txt"];
+ Echo[ "Coil_1_M", Format Table, File > "UI.txt" ];
+ Print[ U, OnRegion Coil_1_M, Format FrequencyTable, File > "UI.txt" ];
+ Print[ I, OnRegion Coil_1_M, Format FrequencyTable, File > "UI.txt"];
+
+ Echo[ "Coil_2_P", Format Table, File > "UI.txt" ];
+ Print[ U, OnRegion Coil_2_P, Format FrequencyTable, File > "UI.txt" ];
+ Print[ I, OnRegion Coil_2_P, Format FrequencyTable, File > "UI.txt"];
+ Echo[ "Coil_2_M", Format Table, File > "UI.txt" ];
+ Print[ U, OnRegion Coil_2_M, Format FrequencyTable, File > "UI.txt" ];
+ Print[ I, OnRegion Coil_2_M, Format FrequencyTable, File > "UI.txt"];
+
+ ElseIf (type_Source == 2)
+ // In text file UI.txt: voltage and current of the primary coil (from E_in)
+ // (real and imaginary parts!)
+ Echo[ "E_in", Format Table, File "UI.txt" ];
+ Print[ U, OnRegion E_in, Format FrequencyTable, File > "UI.txt" ];
+ Print[ I, OnRegion E_in, Format FrequencyTable, File > "UI.txt"];
+
+ // In text file UI.txt: voltage and current of the secondary coil (from R_out)
+ Echo[ "R_out", Format Table, File > "UI.txt" ];
+ Print[ U, OnRegion R_out, Format FrequencyTable, File > "UI.txt" ];
+ Print[ I, OnRegion R_out, Format FrequencyTable, File > "UI.txt"];
+ EndIf
+ }
+ }
+}
diff --git a/Magnetodynamics/transfo_common.pro b/Magnetodynamics/transfo_common.pro
index a116935..53034cc 100644
--- a/Magnetodynamics/transfo_common.pro
+++ b/Magnetodynamics/transfo_common.pro
@@ -1,49 +1,49 @@
-
-// Dimensions
-
-width_Core = 1.;
-height_Core = 1.;
-
-// Thickness along Oz (to be considered for a correct definition of voltage)
-thickness_Core = 1.;
-
-width_Window = 0.5;
-height_Window = 0.5;
-
-width_Core_Leg = (width_Core-width_Window)/2.;
-
-width_Coil_1 = 0.10;
-height_Coil_1 = 0.25;
-gap_Core_Coil_1 = 0.05;
-
-width_Coil_2 = 0.10;
-height_Coil_2 = 0.25;
-gap_Core_Coil_2 = 0.05;
-
-gap_Core_Box_X = 1.;
-gap_Core_Box_Y = 1.;
-
-// Characteristic lenghts (for mesh sizes)
-
-s = 1;
-
-c_Core = width_Core_Leg/10. *s;
-
-c_Coil_1 = height_Coil_1/2/5 *s;
-c_Coil_2 = height_Coil_2/2/5 *s;
-
-c_Box = gap_Core_Box_X/6. *s;
-
-// Physical regions
-
-AIR_EXT = 1001;
-SUR_AIR_EXT = 1002;
-AIR_WINDOW = 1011;
-
-CORE = 1050;
-
-COIL_1_PLUS = 1101;
-COIL_1_MINUS = 1102;
-
-COIL_2_PLUS = 1201;
-COIL_2_MINUS = 1202;
+
+// Dimensions
+
+width_Core = 1.;
+height_Core = 1.;
+
+// Thickness along Oz (to be considered for a correct definition of voltage)
+thickness_Core = 1.;
+
+width_Window = 0.5;
+height_Window = 0.5;
+
+width_Core_Leg = (width_Core-width_Window)/2.;
+
+width_Coil_1 = 0.10;
+height_Coil_1 = 0.25;
+gap_Core_Coil_1 = 0.05;
+
+width_Coil_2 = 0.10;
+height_Coil_2 = 0.25;
+gap_Core_Coil_2 = 0.05;
+
+gap_Core_Box_X = 1.;
+gap_Core_Box_Y = 1.;
+
+// Characteristic lenghts (for mesh sizes)
+
+s = 1;
+
+c_Core = width_Core_Leg/10. *s;
+
+c_Coil_1 = height_Coil_1/2/5 *s;
+c_Coil_2 = height_Coil_2/2/5 *s;
+
+c_Box = gap_Core_Box_X/6. *s;
+
+// Physical regions
+
+AIR_EXT = 1001;
+SUR_AIR_EXT = 1002;
+AIR_WINDOW = 1011;
+
+CORE = 1050;
+
+COIL_1_PLUS = 1101;
+COIL_1_MINUS = 1102;
+
+COIL_2_PLUS = 1201;
+COIL_2_MINUS = 1202;
diff --git a/Magnetostatics/electromagnet.geo b/Magnetostatics/electromagnet.geo
index 7bd410c..b24c084 100644
--- a/Magnetostatics/electromagnet.geo
+++ b/Magnetostatics/electromagnet.geo
@@ -1,54 +1,54 @@
-/* -------------------------------------------------------------------
- File "electromagnet.geo"
-
- This file is the geometrical description used by GMSH to produce
- the file "electromagnet.msh".
- ------------------------------------------------------------------- */
-
-dxCore = 50.e-3; dyCore = 100.e-3;
-xInd = 75.e-3; dxInd = 25.e-3; dyInd = 50.e-3;
-
-Include "electromagnet_common.pro";
-
-s = DefineNumber[1, Name "Model parameters/Global mesh size",
- Help "Reduce for finer mesh"];
-p0 = 12.e-3 *s;
-pCorex = 4.e-3 *s; pCorey0 = 8.e-3 *s; pCorey = 4.e-3 *s;
-pIndx = 5.e-3 *s; pIndy = 5.e-3 *s;
-pInt = 12.5e-3*s; pExt = 12.5e-3*s;
-
-Point(1) = {0,0,0,p0};
-Point(2) = {dxCore,0,0,pCorex};
-Point(3) = {dxCore,dyCore,0,pCorey};
-Point(4) = {0,dyCore,0,pCorey0};
-Point(5) = {xInd,0,0,pIndx};
-Point(6) = {xInd+dxInd,0,0,pIndx};
-Point(7) = {xInd+dxInd,dyInd,0,pIndy};
-Point(8) = {xInd,dyInd,0,pIndy};
-Point(9) = {rInt,0,0,pInt};
-Point(10) = {rExt,0,0,pExt};
-Point(11) = {0,rInt,0,pInt};
-Point(12) = {0,rExt,0,pExt};
-
-Line(1) = {1,2}; Line(2) = {2,5}; Line(3) = {5,6};
-Line(4) = {6,9}; Line(5) = {9,10}; Line(6) = {1,4};
-Line(7) = {4,11}; Line(8) = {11,12}; Line(9) = {2,3};
-Line(10) = {3,4}; Line(11) = {6,7}; Line(12) = {7,8};
-Line(13) = {8,5};
-
-Circle(14) = {9,1,11}; Circle(15) = {10,1,12};
-
-Line Loop(16) = {-6,1,9,10}; Plane Surface(17) = {16};
-Line Loop(18) = {11,12,13,3}; Plane Surface(19) = {18};
-Line Loop(20) = {7,-14,-4,11,12,13,-2,9,10}; Plane Surface(21) = {-20}; // "-" for orientation
-Line Loop(22) = {8,-15,-5,14}; Plane Surface(23) = {-22};
-
-Physical Surface(101) = {21}; /* Air */
-Physical Surface(102) = {17}; /* Core */
-Physical Surface(103) = {19}; /* Ind */
-Physical Surface(111) = {23}; /* AirInf */
-
-Physical Line(1100) = {1,2,3,4,5}; /* Surface ht = 0 */
-Physical Line(1101) = {6,7,8}; /* Surface bn = 0 */
-Physical Line(1102) = {15}; /* Surface Inf */
-
+/* -------------------------------------------------------------------
+ File "electromagnet.geo"
+
+ This file is the geometrical description used by GMSH to produce
+ the file "electromagnet.msh".
+ ------------------------------------------------------------------- */
+
+dxCore = 50.e-3; dyCore = 100.e-3;
+xInd = 75.e-3; dxInd = 25.e-3; dyInd = 50.e-3;
+
+Include "electromagnet_common.pro";
+
+s = DefineNumber[1, Name "Model parameters/Global mesh size",
+ Help "Reduce for finer mesh"];
+p0 = 12.e-3 *s;
+pCorex = 4.e-3 *s; pCorey0 = 8.e-3 *s; pCorey = 4.e-3 *s;
+pIndx = 5.e-3 *s; pIndy = 5.e-3 *s;
+pInt = 12.5e-3*s; pExt = 12.5e-3*s;
+
+Point(1) = {0,0,0,p0};
+Point(2) = {dxCore,0,0,pCorex};
+Point(3) = {dxCore,dyCore,0,pCorey};
+Point(4) = {0,dyCore,0,pCorey0};
+Point(5) = {xInd,0,0,pIndx};
+Point(6) = {xInd+dxInd,0,0,pIndx};
+Point(7) = {xInd+dxInd,dyInd,0,pIndy};
+Point(8) = {xInd,dyInd,0,pIndy};
+Point(9) = {rInt,0,0,pInt};
+Point(10) = {rExt,0,0,pExt};
+Point(11) = {0,rInt,0,pInt};
+Point(12) = {0,rExt,0,pExt};
+
+Line(1) = {1,2}; Line(2) = {2,5}; Line(3) = {5,6};
+Line(4) = {6,9}; Line(5) = {9,10}; Line(6) = {1,4};
+Line(7) = {4,11}; Line(8) = {11,12}; Line(9) = {2,3};
+Line(10) = {3,4}; Line(11) = {6,7}; Line(12) = {7,8};
+Line(13) = {8,5};
+
+Circle(14) = {9,1,11}; Circle(15) = {10,1,12};
+
+Line Loop(16) = {-6,1,9,10}; Plane Surface(17) = {16};
+Line Loop(18) = {11,12,13,3}; Plane Surface(19) = {18};
+Line Loop(20) = {7,-14,-4,11,12,13,-2,9,10}; Plane Surface(21) = {-20}; // "-" for orientation
+Line Loop(22) = {8,-15,-5,14}; Plane Surface(23) = {-22};
+
+Physical Surface(101) = {21}; /* Air */
+Physical Surface(102) = {17}; /* Core */
+Physical Surface(103) = {19}; /* Ind */
+Physical Surface(111) = {23}; /* AirInf */
+
+Physical Line(1100) = {1,2,3,4,5}; /* Surface ht = 0 */
+Physical Line(1101) = {6,7,8}; /* Surface bn = 0 */
+Physical Line(1102) = {15}; /* Surface Inf */
+
diff --git a/Magnetostatics/electromagnet.pro b/Magnetostatics/electromagnet.pro
index 629379f..1e1c1c4 100644
--- a/Magnetostatics/electromagnet.pro
+++ b/Magnetostatics/electromagnet.pro
@@ -1,267 +1,267 @@
-/* -------------------------------------------------------------------
- Tutorial 2 : magnetostatic field of an electromagnet
-
- Features:
- - Infinite ring geometrical transformation
- - Parameters shared by Gmsh and GetDp, and Onelab parameters
- - FunctionSpaces for the 2D vector potential formulation
-
- To compute the solution in a terminal:
- getdp electromagnet -solve MagSta_a
- getdp electromagnet -pos Map_a
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > electromagnet.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-/* Electromagnetic fields expand to infinity.
- The corresponding boundary condition can be imposed rigorously
- by means of a gometrical transformation that maps a ring (or shell) of finite elements
- to the complementary of its interior.
- As this is a mere geometric transformation,
- it is enough in the model description to attribute a special jacobian
- to the ring region ("AirInf"). See Jacobian{} section below.
- With this information, GetDP is able to deal with the correct transformation
- of all quantities involved in the model.
-
- The special jacobian "VolSphShell" has parameters.
- There are 2 parameters in this case, "Val_Rint" and "Val_Rext",
- which represent the inner and outer radii of the transformed ring region
- and whose value must match those used
- in the geometrical description of the model (.geo file).
- This is a typical case where Gmsh and GetDP must consistently share parameter values.
- To ensure consistency in all cases, common parameters are defined
- is a specific file "electromagnet_common.pro",
- which is included in both the .geo and .pro file of the model.
-
- Besides sharing parameters between Gmsh and GetDP,
- it is also useful to share some parameters (not all) with the user of the model,
- i.e., to make them editable in the GUI before running the model.
- Such variables are called Onelab variables (because the sharing mechanism
- between the model and the GUI uses the Onelab interface).
- Onelab parameters are defined with a "DefineNumber" statement,
- which can be invoked in the .geo, .pro, or _common.pro files.
- */
-
-
-Group {
- // Physical regions:
- Air = Region[ 101 ]; Core = Region[ 102 ];
- Ind = Region[ 103 ]; AirInf = Region[ 111 ];
-
- Surface_ht0 = Region[ 1100 ];
- Surface_bn0 = Region[ 1101 ];
- Surface_Inf = Region[ 1102 ];
-
-
- /* Abstract regions :
- The purpose of abstract regions is to allow a generic definition of
- the FunctionSpace, Formulation and PostProcessing fields
- with no reference to model-specific Physical regions.
- We will show in a later tutorial how abstract formulations can then be isolated
- in geometry independent template files, thanks to an appropriate declaration mechanism
- (using DefineConstant[], DefineGroup[] and DefineFunction[]).
-
- The abstract regions in this model have the following interpretation:
- - Vol_Nu_Mag = region where the term [ nu[] * Dof{d a} , {d a} ] is assembled
- - Vol_Js_Mag = region where the term [ - Dof{js} , {a} ] is assembled
- - Vol_Inf_Mag = region where the infinite ring geometric transformation is applied
- - Sur_Dir_Mag = Homogeneous Dirichlet part of the model's boundary;
- - Sur_Neu_Mag = Homogeneous Neumann part of the model's boundary;
- */
- Vol_Nu_Mag = Region[ {Air, AirInf, Core, Ind} ];
- Vol_Js_Mag = Region[ Ind ];
- Vol_Inf_Mag = Region[ {AirInf} ];
- Sur_Dir_Mag = Region[ {Surface_bn0, Surface_Inf} ];
- Sur_Neu_Mag = Region[ {Surface_ht0} ];
-}
-
-Function {
- mu0 = 4.e-7 * Pi;
- murCore = DefineNumber[100, Name "Model parameters/Mur core",
- Help "Magnetic relative permeability of Core"];
-
- nu [ Region[{Air, Ind, AirInf}] ] = 1. / mu0;
- nu [ Core ] = 1. / (murCore * mu0);
-
- NbTurns = 1000 ;
- Current = DefineNumber[0.01, Name "Model parameters/Current",
- Help "Current injected in coil [A]"];
- Js_fct[ Ind ] = -NbTurns*Current/SurfaceArea[];
- /* The minus sign is to have the current in -e_z direction,
- so that the magnetic induction field is in +e_y direction */
-}
-
-/* In the 2D approximation, the magnetic vector potential A and the current density Js
- are not scalars, but vectors with a z-component only:
- A = Vector [ 0, 0, az(x,y,t) ]
- Js = Vector [ 0, 0, jsz(x,y,t) ]
- In order to compute derivatives and apply geometric transformations adequately,
- GetDP needs this information.
- Regarding discretization, now, A is node-based, whereas Js is region-wise constant.
- Considering all this, one ends then up with the FunctionSpaces
- "Hcurl_a_Mag_2D" and "Hregion_j_Mag_2D" as they are defined below.
-
- The function space "Hregion_j_Mag_2D" provides one basis function,
- and hence one degree of freedom, per physical region in the abstract region "Vol_Js_Mag".
- The constraint "SourceCurrentDensityZ" fixes all these dofs,
- so the FunctionSpace "Hregion_j_Mag_2D" is fully fixed and has no FE unknowns.
- One could thus have replaced it by a simple function
- and the Galerkin term would have been
-
- Galerkin { [ Vector[ 0,0,-Js_fct[] ] , {a} ]; In Vol_Js_Mag;
- Jacobian Vol; Integration Int; }
-
- instead of
-
- Galerkin { [ - Dof{js} , {a} ]; In Vol_Js_Mag;
- Jacobian Vol; Integration Int; }
-
- Thechosen implementation below is however more effeicient
- as it avoids evaluating repeatedly the function Js_fct[] during assembly.
- */
-
-
-Constraint {
- { Name Dirichlet_a_Mag;
- Case {
- { Region Sur_Dir_Mag ; Value 0.; }
- }
- }
- { Name SourceCurrentDensityZ;
- Case {
- { Region Vol_Js_Mag ; Value Js_fct[]; }
- }
- }
-}
-
-Group {
- Dom_Hcurl_a_Mag_2D = Region[ {Vol_Nu_Mag, Sur_Neu_Mag} ];
-}
-FunctionSpace {
- { Name Hcurl_a_Mag_2D; Type Form1P; // Magnetic vector potential A
- BasisFunction {
- { Name se; NameOfCoef ae; Function BF_PerpendicularEdge;
- Support Dom_Hcurl_a_Mag_2D ; Entity NodesOf[ All ]; }
- }
- Constraint {
- { NameOfCoef ae; EntityType NodesOf;
- NameOfConstraint Dirichlet_a_Mag; }
- }
- }
-
- { Name Hregion_j_Mag_2D; Type Vector; // Electric current density Js
- BasisFunction {
- { Name sr; NameOfCoef jsr; Function BF_RegionZ;
- Support Vol_Js_Mag; Entity Vol_Js_Mag; }
- }
- Constraint {
- { NameOfCoef jsr; EntityType Region;
- NameOfConstraint SourceCurrentDensityZ; }
- }
- }
-
-}
-
-Include "electromagnet_common.pro";
-Val_Rint = rInt; Val_Rext = rExt;
-Jacobian {
- { Name Vol ;
- Case { { Region Vol_Inf_Mag ;
- Jacobian VolSphShell {Val_Rint, Val_Rext} ; }
- { Region All ; Jacobian Vol ; }
- }
- }
-}
-
-Integration {
- { Name Int ;
- Case { {Type Gauss ;
- Case { { GeoElement Triangle ; NumberOfPoints 4 ; }
- { GeoElement Quadrangle ; NumberOfPoints 4 ; }
- }
- }
- }
- }
-}
-
-Formulation {
- { Name Magnetostatics_a_2D; Type FemEquation;
- Quantity {
- { Name a ; Type Local; NameOfSpace Hcurl_a_Mag_2D; }
- { Name js; Type Local; NameOfSpace Hregion_j_Mag_2D; }
- }
- Equation {
- Galerkin { [ nu[] * Dof{d a} , {d a} ]; In Vol_Nu_Mag;
- Jacobian Vol; Integration Int; }
- Galerkin { [ -Dof{js} , {a} ]; In Vol_Js_Mag;
- Jacobian Vol; Integration Int; }
- }
- }
-}
-
-Resolution {
- { Name MagSta_a;
- System {
- { Name Sys_Mag; NameOfFormulation Magnetostatics_a_2D; }
- }
- Operation {
- Generate[Sys_Mag]; Solve[Sys_Mag]; SaveSolution[Sys_Mag];
- }
- }
-}
-
-PostProcessing {
- { Name MagSta_a_2D; NameOfFormulation Magnetostatics_a_2D;
- Quantity {
- { Name a;
- Value {
- Local { [ {a} ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
- }
- }
- { Name az;
- Value {
- Local { [ CompZ[{a}] ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
- }
- }
- { Name b;
- Value {
- Local { [ {d a} ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
- }
- }
- { Name h;
- Value {
- Local { [ nu[] * {d a} ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
- }
- }
- { Name js;
- Value {
- Local { [ {js} ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
- }
- }
- }
- }
-}
-
-e = 1.e-5;
-h = 0.02;
-p1 = {e,h,0};
-p2 = {0.25-e,h,0}; // horizontal cut through model, just above x-axis.
-
-PostOperation {
-
- { Name Map_a; NameOfPostProcessing MagSta_a_2D;
- Operation {
- Echo[ Str["l=PostProcessing.NbViews-1;",
- "View[l].IntervalsType = 1;",
- "View[l].NbIso = 40;"],
- File "tmp.geo", LastTimeStepOnly] ;
- Print[ a, OnElementsOf Dom_Hcurl_a_Mag_2D, File "a.pos" ];
- Print[ js, OnElementsOf Dom_Hcurl_a_Mag_2D, File "js.pos" ];
- Print[ az, OnElementsOf Dom_Hcurl_a_Mag_2D, File "az.pos" ];
- Print[ b, OnElementsOf Dom_Hcurl_a_Mag_2D, File "b.pos" ];
- Print[ b, OnLine{{List[p1]}{List[p2]}} {50}, File "by.pos" ];
- }
- }
-}
+/* -------------------------------------------------------------------
+ Tutorial 2 : magnetostatic field of an electromagnet
+
+ Features:
+ - Infinite ring geometrical transformation
+ - Parameters shared by Gmsh and GetDp, and Onelab parameters
+ - FunctionSpaces for the 2D vector potential formulation
+
+ To compute the solution in a terminal:
+ getdp electromagnet -solve MagSta_a
+ getdp electromagnet -pos Map_a
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > electromagnet.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+/* Electromagnetic fields expand to infinity.
+ The corresponding boundary condition can be imposed rigorously
+ by means of a gometrical transformation that maps a ring (or shell) of finite elements
+ to the complementary of its interior.
+ As this is a mere geometric transformation,
+ it is enough in the model description to attribute a special jacobian
+ to the ring region ("AirInf"). See Jacobian{} section below.
+ With this information, GetDP is able to deal with the correct transformation
+ of all quantities involved in the model.
+
+ The special jacobian "VolSphShell" has parameters.
+ There are 2 parameters in this case, "Val_Rint" and "Val_Rext",
+ which represent the inner and outer radii of the transformed ring region
+ and whose value must match those used
+ in the geometrical description of the model (.geo file).
+ This is a typical case where Gmsh and GetDP must consistently share parameter values.
+ To ensure consistency in all cases, common parameters are defined
+ is a specific file "electromagnet_common.pro",
+ which is included in both the .geo and .pro file of the model.
+
+ Besides sharing parameters between Gmsh and GetDP,
+ it is also useful to share some parameters (not all) with the user of the model,
+ i.e., to make them editable in the GUI before running the model.
+ Such variables are called Onelab variables (because the sharing mechanism
+ between the model and the GUI uses the Onelab interface).
+ Onelab parameters are defined with a "DefineNumber" statement,
+ which can be invoked in the .geo, .pro, or _common.pro files.
+ */
+
+
+Group {
+ // Physical regions:
+ Air = Region[ 101 ]; Core = Region[ 102 ];
+ Ind = Region[ 103 ]; AirInf = Region[ 111 ];
+
+ Surface_ht0 = Region[ 1100 ];
+ Surface_bn0 = Region[ 1101 ];
+ Surface_Inf = Region[ 1102 ];
+
+
+ /* Abstract regions :
+ The purpose of abstract regions is to allow a generic definition of
+ the FunctionSpace, Formulation and PostProcessing fields
+ with no reference to model-specific Physical regions.
+ We will show in a later tutorial how abstract formulations can then be isolated
+ in geometry independent template files, thanks to an appropriate declaration mechanism
+ (using DefineConstant[], DefineGroup[] and DefineFunction[]).
+
+ The abstract regions in this model have the following interpretation:
+ - Vol_Nu_Mag = region where the term [ nu[] * Dof{d a} , {d a} ] is assembled
+ - Vol_Js_Mag = region where the term [ - Dof{js} , {a} ] is assembled
+ - Vol_Inf_Mag = region where the infinite ring geometric transformation is applied
+ - Sur_Dir_Mag = Homogeneous Dirichlet part of the model's boundary;
+ - Sur_Neu_Mag = Homogeneous Neumann part of the model's boundary;
+ */
+ Vol_Nu_Mag = Region[ {Air, AirInf, Core, Ind} ];
+ Vol_Js_Mag = Region[ Ind ];
+ Vol_Inf_Mag = Region[ {AirInf} ];
+ Sur_Dir_Mag = Region[ {Surface_bn0, Surface_Inf} ];
+ Sur_Neu_Mag = Region[ {Surface_ht0} ];
+}
+
+Function {
+ mu0 = 4.e-7 * Pi;
+ murCore = DefineNumber[100, Name "Model parameters/Mur core",
+ Help "Magnetic relative permeability of Core"];
+
+ nu [ Region[{Air, Ind, AirInf}] ] = 1. / mu0;
+ nu [ Core ] = 1. / (murCore * mu0);
+
+ NbTurns = 1000 ;
+ Current = DefineNumber[0.01, Name "Model parameters/Current",
+ Help "Current injected in coil [A]"];
+ Js_fct[ Ind ] = -NbTurns*Current/SurfaceArea[];
+ /* The minus sign is to have the current in -e_z direction,
+ so that the magnetic induction field is in +e_y direction */
+}
+
+/* In the 2D approximation, the magnetic vector potential A and the current density Js
+ are not scalars, but vectors with a z-component only:
+ A = Vector [ 0, 0, az(x,y,t) ]
+ Js = Vector [ 0, 0, jsz(x,y,t) ]
+ In order to compute derivatives and apply geometric transformations adequately,
+ GetDP needs this information.
+ Regarding discretization, now, A is node-based, whereas Js is region-wise constant.
+ Considering all this, one ends then up with the FunctionSpaces
+ "Hcurl_a_Mag_2D" and "Hregion_j_Mag_2D" as they are defined below.
+
+ The function space "Hregion_j_Mag_2D" provides one basis function,
+ and hence one degree of freedom, per physical region in the abstract region "Vol_Js_Mag".
+ The constraint "SourceCurrentDensityZ" fixes all these dofs,
+ so the FunctionSpace "Hregion_j_Mag_2D" is fully fixed and has no FE unknowns.
+ One could thus have replaced it by a simple function
+ and the Integral term would have been
+
+ Integral { [ Vector[ 0,0,-Js_fct[] ] , {a} ]; In Vol_Js_Mag;
+ Jacobian Vol; Integration Int; }
+
+ instead of
+
+ Integral { [ - Dof{js} , {a} ]; In Vol_Js_Mag;
+ Jacobian Vol; Integration Int; }
+
+ Thechosen implementation below is however more effeicient
+ as it avoids evaluating repeatedly the function Js_fct[] during assembly.
+ */
+
+
+Constraint {
+ { Name Dirichlet_a_Mag;
+ Case {
+ { Region Sur_Dir_Mag ; Value 0.; }
+ }
+ }
+ { Name SourceCurrentDensityZ;
+ Case {
+ { Region Vol_Js_Mag ; Value Js_fct[]; }
+ }
+ }
+}
+
+Group {
+ Dom_Hcurl_a_Mag_2D = Region[ {Vol_Nu_Mag, Sur_Neu_Mag} ];
+}
+FunctionSpace {
+ { Name Hcurl_a_Mag_2D; Type Form1P; // Magnetic vector potential A
+ BasisFunction {
+ { Name se; NameOfCoef ae; Function BF_PerpendicularEdge;
+ Support Dom_Hcurl_a_Mag_2D ; Entity NodesOf[ All ]; }
+ }
+ Constraint {
+ { NameOfCoef ae; EntityType NodesOf;
+ NameOfConstraint Dirichlet_a_Mag; }
+ }
+ }
+
+ { Name Hregion_j_Mag_2D; Type Vector; // Electric current density Js
+ BasisFunction {
+ { Name sr; NameOfCoef jsr; Function BF_RegionZ;
+ Support Vol_Js_Mag; Entity Vol_Js_Mag; }
+ }
+ Constraint {
+ { NameOfCoef jsr; EntityType Region;
+ NameOfConstraint SourceCurrentDensityZ; }
+ }
+ }
+
+}
+
+Include "electromagnet_common.pro";
+Val_Rint = rInt; Val_Rext = rExt;
+Jacobian {
+ { Name Vol ;
+ Case { { Region Vol_Inf_Mag ;
+ Jacobian VolSphShell {Val_Rint, Val_Rext} ; }
+ { Region All ; Jacobian Vol ; }
+ }
+ }
+}
+
+Integration {
+ { Name Int ;
+ Case { {Type Gauss ;
+ Case { { GeoElement Triangle ; NumberOfPoints 4 ; }
+ { GeoElement Quadrangle ; NumberOfPoints 4 ; }
+ }
+ }
+ }
+ }
+}
+
+Formulation {
+ { Name Magnetostatics_a_2D; Type FemEquation;
+ Quantity {
+ { Name a ; Type Local; NameOfSpace Hcurl_a_Mag_2D; }
+ { Name js; Type Local; NameOfSpace Hregion_j_Mag_2D; }
+ }
+ Equation {
+ Integral { [ nu[] * Dof{d a} , {d a} ]; In Vol_Nu_Mag;
+ Jacobian Vol; Integration Int; }
+ Integral { [ -Dof{js} , {a} ]; In Vol_Js_Mag;
+ Jacobian Vol; Integration Int; }
+ }
+ }
+}
+
+Resolution {
+ { Name MagSta_a;
+ System {
+ { Name Sys_Mag; NameOfFormulation Magnetostatics_a_2D; }
+ }
+ Operation {
+ Generate[Sys_Mag]; Solve[Sys_Mag]; SaveSolution[Sys_Mag];
+ }
+ }
+}
+
+PostProcessing {
+ { Name MagSta_a_2D; NameOfFormulation Magnetostatics_a_2D;
+ Quantity {
+ { Name a;
+ Value {
+ Local { [ {a} ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
+ }
+ }
+ { Name az;
+ Value {
+ Local { [ CompZ[{a}] ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
+ }
+ }
+ { Name b;
+ Value {
+ Local { [ {d a} ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
+ }
+ }
+ { Name h;
+ Value {
+ Local { [ nu[] * {d a} ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
+ }
+ }
+ { Name js;
+ Value {
+ Local { [ {js} ]; In Dom_Hcurl_a_Mag_2D; Jacobian Vol; }
+ }
+ }
+ }
+ }
+}
+
+e = 1.e-5;
+h = 0.02;
+p1 = {e,h,0};
+p2 = {0.25-e,h,0}; // horizontal cut through model, just above x-axis.
+
+PostOperation {
+
+ { Name Map_a; NameOfPostProcessing MagSta_a_2D;
+ Operation {
+ Echo[ Str["l=PostProcessing.NbViews-1;",
+ "View[l].IntervalsType = 1;",
+ "View[l].NbIso = 40;"],
+ File "tmp.geo", LastTimeStepOnly] ;
+ Print[ a, OnElementsOf Dom_Hcurl_a_Mag_2D, File "a.pos" ];
+ Print[ js, OnElementsOf Dom_Hcurl_a_Mag_2D, File "js.pos" ];
+ Print[ az, OnElementsOf Dom_Hcurl_a_Mag_2D, File "az.pos" ];
+ Print[ b, OnElementsOf Dom_Hcurl_a_Mag_2D, File "b.pos" ];
+ Print[ b, OnLine{{List[p1]}{List[p2]}} {50}, File "by.pos" ];
+ }
+ }
+}
diff --git a/Magnetostatics/electromagnet_common.pro b/Magnetostatics/electromagnet_common.pro
index 56879cd..f0dd285 100644
--- a/Magnetostatics/electromagnet_common.pro
+++ b/Magnetostatics/electromagnet_common.pro
@@ -1,4 +1,4 @@
-// Parameters shared by Gmsh and GetDP
-
-rInt = 200.e-3;
-rExt = 250.e-3;
+// Parameters shared by Gmsh and GetDP
+
+rInt = 200.e-3;
+rExt = 250.e-3;
diff --git a/PotentialFlow/magnus.geo b/PotentialFlow/magnus.geo
index c78c6ac..3d477a7 100644
--- a/PotentialFlow/magnus.geo
+++ b/PotentialFlow/magnus.geo
@@ -1,71 +1,71 @@
-Include "magnus_common.pro";
-
-A = (BoxSize-1)/2.;
-B = A;
-R = 0.5;
-lc = A/10;
-
-
-If( Flag_Object == 0 ) // Cylinder
-
-lcr = 0.1;
-Point(1) = { 2*R, 0.0, 0.0, lcr};
-Point(2) = { R, -R, 0.0, lcr};
-Point(3) = { 0.0, 0.0, 0.0, lcr};
-Point(4) = { R, R, 0.0 , lcr};
-Point(5) = { R, 0.0, 0.0 , lcr};
-Circle(1) = {1,5,2};
-Circle(2) = {2,5,3};
-Circle(3) = {3,5,4};
-Circle(4) = {4,5,1};
-
-// Points to be connected with the outer boundary
-PtA = 4;
-PtB = 2;
-
-Else // naca airfoil
-
-lca = 0.03;
-Include "nacaAirFoil.geo";
-PtA = 121;
-PtB = 81;
-
-EndIf
-
-Point(306) = { 0, B, 0, lc};
-Point(307) = { 0,-B, 0, lc};
-
-Line(5) = { PtA, 306 };
-Line(6) = { PtB, 307 };
-
-Point(308) = {-A,-B, 0, lc};
-Point(309) = {-A, B, 0, lc};
-Point(310) = { A+1, B, 0, lc};
-Point(311) = { A+1,-B, 0, lc};
-
-Line( 7) = { 306, 309 };
-Line( 8) = { 309, 308 };
-Line( 9) = { 308, 307 };
-Line(10) = { 307, 311 };
-Line(11) = { 311, 310 };
-Line(12) = { 310, 306 };
-
-Line Loop(21) = { 7, 8, 9, -6, 2, 3, 5 }; // aire a gauche
-Line Loop(22) = { 10, 11, 12, -5, 4, 1, 6 };
-
-Plane Surface(24) = { 21 };
-Plane Surface(25) = { 22 };
-
-Physical Surface("Fluid", 2) = { 24, 25 };
-Physical Line("UpStream", 10) = { 8 };
-Physical Line("DownStream", 11) = { 11 };
-Physical Line("Airfoil", 12) = { 1 ... 4 };
-Physical Line("Wake", 13) = { 5 };
-
-
-
-//Line Loop(20) = {1,2,3,4};
-//Plane Surface(23) = {20};
-//Physical Surface("Cylinder", 1) = {23};
-//Physical Line("Outer", 10) = { 7 ... 12 };
-
+Include "magnus_common.pro";
+
+A = (BoxSize-1)/2.;
+B = A;
+R = 0.5;
+lc = A/10;
+
+
+If( Flag_Object == 0 ) // Cylinder
+
+lcr = 0.1;
+Point(1) = { 2*R, 0.0, 0.0, lcr};
+Point(2) = { R, -R, 0.0, lcr};
+Point(3) = { 0.0, 0.0, 0.0, lcr};
+Point(4) = { R, R, 0.0 , lcr};
+Point(5) = { R, 0.0, 0.0 , lcr};
+Circle(1) = {1,5,2};
+Circle(2) = {2,5,3};
+Circle(3) = {3,5,4};
+Circle(4) = {4,5,1};
+
+// Points to be connected with the outer boundary
+PtA = 4;
+PtB = 2;
+
+Else // naca airfoil
+
+lca = 0.03;
+Include "nacaAirFoil.geo";
+PtA = 121;
+PtB = 81;
+
+EndIf
+
+Point(306) = { 0, B, 0, lc};
+Point(307) = { 0,-B, 0, lc};
+
+Line(5) = { PtA, 306 };
+Line(6) = { PtB, 307 };
+
+Point(308) = {-A,-B, 0, lc};
+Point(309) = {-A, B, 0, lc};
+Point(310) = { A+1, B, 0, lc};
+Point(311) = { A+1,-B, 0, lc};
+
+Line( 7) = { 306, 309 };
+Line( 8) = { 309, 308 };
+Line( 9) = { 308, 307 };
+Line(10) = { 307, 311 };
+Line(11) = { 311, 310 };
+Line(12) = { 310, 306 };
+
+Line Loop(21) = { 7, 8, 9, -6, 2, 3, 5 }; // aire a gauche
+Line Loop(22) = { 10, 11, 12, -5, 4, 1, 6 };
+
+Plane Surface(24) = { 21 };
+Plane Surface(25) = { 22 };
+
+Physical Surface("Fluid", 2) = { 24, 25 };
+Physical Line("UpStream", 10) = { 8 };
+Physical Line("DownStream", 11) = { 11 };
+Physical Line("Airfoil", 12) = { 1 ... 4 };
+Physical Line("Wake", 13) = { 5 };
+
+
+
+//Line Loop(20) = {1,2,3,4};
+//Plane Surface(23) = {20};
+//Physical Surface("Cylinder", 1) = {23};
+//Physical Line("Outer", 10) = { 7 ... 12 };
+
diff --git a/PotentialFlow/magnus.pro b/PotentialFlow/magnus.pro
index 8319076..d3fa9a0 100644
--- a/PotentialFlow/magnus.pro
+++ b/PotentialFlow/magnus.pro
@@ -1,429 +1,420 @@
-/* -------------------------------------------------------------------
- Tutorial 6 : Potential flow and Magnus effect
-
- Features:
- - Potential flow, irrotational flow
- - Multivalued scalar field
- - Lift and Magnus effect, stagnation points
- - Run-time variables
- - Elementary algorithms in the Resolution section
- - Non-linear iteration to achieve Kutta's condition
-
- To compute the solution in a terminal:
- getdp magnus.pro -solve PotentialFlow -pos PotentialFlow
- gmsh magnus.geo velocity.pos
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > magnus.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-/*
- This model solves a 2D potential flow around a cylinder or a naca airfoil
- placed in a uniform "V_infinity" flow.
- Potential flows are defined by
-
- V = grad phi => curl V = 0
-
- where the multivalued scalar potential "phi"
- presents a discontinuity of magnitude "deltaPhi"
- across a cut "Sur_Cut".
- In consequence, the velocity field "V" is curl-free
- over the wole domain of analysis "Vol_rho"
- but its circulation over any closed curve circling around the object,
- a quantity often noted "Gamma" in the literature,
- gives "deltaPhi" as a result.
- The circulation of "V" over closed curves
- not circling around the object is zero.
-
- In the getDP model, the discontinuity "deltaPhi" [m^2/s]
- is defined as a global quantity in the Functional space of "phi".
- The associated (dual) global quantity is the mass flow density,
- noted "Dmdt", which has [kg/s] as a unit.
-
- Governing equations are
-
- div ( rho[] grad phi ) = 0 in Vol_rho
- rho[] grad phi . n = rho[] Vn = 0 on Sur_Neu
-
- whereas the uniform velocity field "V_infinity" is imposed
- by means of Dirichlet boundary conditions
- on the upstream and downstream surfaces "GammaUp" and "GammaDown".
-
- Momentum equation is decoupled in case of stationary potential flows.
- The velocity filed can be solved first, and the pressure
- is obtained afterwards by invoking Bernoulli's theorem:
-
- p = -0.5 * rho[] * SquNorm [ {d phi} ]
-
- The "Lift" force in "Y" direction is then evaluated
- either by integrating "p * CompY[Normal[]]"
- over the contour of the object,
- or by the Kutta-Jukowski theorem
-
- Lift = - L_z rho[] V_infinity Gamma
-
- which is a first order approximation of the former.
-
- "Cylinder" case:
- Either the circulation "deltaPhi" or the mass flow rate "Dmdt"
- can be imposed, according to the "Flag_Circ" flag.
- The Lift is evaluated by both the integration of pressure
- and the Kutta-Jukowski approximation.
-
- "Airfoil" case:
- If "Flag_Circ == 1", the model works similar to the "Cylinder" case.
- If "Flag_Circ == 0", the mass flow rate is not directly imposed
- in this case.
- It is determined so that the Kutta condition is verified.
- This condition states that the actual value of "Dmdt"
- is the one for which the stagnation point
- (singularity of the velocity field)
- is located at the trailing edge of the airfoil,.
- This is true when the function
-
- argVTrail[] = ( Atan2[CompY[$1], CompX[$1] ] - Incidence ) / deg ;
-
- returns zero when evaluated for the velocity at a point "P_edge"
- close to the trailing edge of the airfoil.
- A non linear iteration is thus done by means of a pseudo-newton scheme,
- updating the value of the imposed "Dmdt" until the norm of the residual
-
- f(V) = argVTrail[ {d phi } ] OnPoint {1.0001,0,0}
-
- comes below a fixed tolerance.
- */
-
-Include "magnus_common.pro";
-
-Group{
- // Physical regions
- Fluid = Region[ 2 ];
- GammaUp = Region[ 10 ];
- GammaDown = Region[ 11 ];
- GammaAirf = Region[ 12 ];
- GammaCut = Region[ 13 ];
-
- // Abstract regions
- Vol_rho = Region[ { Fluid } ];
- Sur_Dir = Region[ { GammaUp, GammaDown } ];
- Sur_Neu = Region[ { GammaAirf } ];
- Sur_Cut = Region[ { GammaCut } ];
-}
-
-Function{
- rho[] = 1.225; // kg/m^3
- MassFlowRate[] = MassFlowRate; // kg/s
- DeltaPhi[] = DeltaPhi; // m^2/s
- argVTrail[] = ( Atan2[CompY[$1], CompX[$1] ] - Incidence ) / deg ;
-}
-
-Jacobian {
- { Name Vol ;
- Case {
- { Region All ; Jacobian Vol ; }
- }
- }
- { Name Sur ;
- Case {
- { Region All ; Jacobian Sur ; }
- }
- }
-}
-
-Integration {
- { Name Int ;
- Case {
- { Type Gauss ;
- Case {
- { GeoElement Point ; NumberOfPoints 1 ; }
- { GeoElement Line ; NumberOfPoints 4 ; }
- { GeoElement Triangle ; NumberOfPoints 6 ; }
- { GeoElement Quadrangle ; NumberOfPoints 7 ; }
- { GeoElement Tetrahedron ; NumberOfPoints 15 ; }
- { GeoElement Hexahedron ; NumberOfPoints 34 ; }
- }
- }
- }
- }
-}
-
-Constraint{
- { Name Dirichlet; Type Assign;
- Case{
- // Boundary conditions for the V_infinity uniform flow
- { Region GammaDown; Value Velocity*BoxSize; }
- { Region GammaUp ; Value 0; }
- }
- }
- { Name DeltaPhi; Type Assign;
- Case{
- { Region Sur_Cut; Value DeltaPhi[]; }
- }
- }
- { Name MassFlowRate; Type Assign;
- Case{
- { Region Sur_Cut; Value MassFlowRate[]; }
- }
- }
-}
-
-// Domains of definition used in the description of the function space
-// These groups contain both volume and surface regions/elements.
-Group{
- Dom_Vh = Region[ { Vol_rho, Sur_Dir, Sur_Neu, Sur_Cut } ];
- Dom_Cut = ElementsOf[ Dom_Vh, OnPositiveSideOf Sur_Cut ];
-}
-FunctionSpace{
- { Name Vh; Type Form0;
- BasisFunction{
- { Name vn; NameOfCoef phin; Function BF_Node;
- Support Dom_Vh; Entity NodesOf[All]; }
- { Name vc; NameOfCoef dphi; Function BF_GroupOfNodes;
- Support Dom_Cut; Entity GroupsOfNodesOf[ Sur_Cut ];}
- }
- SubSpace {
- { Name phiCont ; NameOfBasisFunction { vn } ; }
- { Name phiDisc ; NameOfBasisFunction { vc } ; }
- }
- GlobalQuantity {
- { Name Circ ; Type AliasOf ; NameOfCoef dphi ; }
- { Name Dmdt ; Type AssociatedWith ; NameOfCoef dphi ; }
- }
- Constraint{
- {NameOfCoef phin; EntityType NodesOf;
- NameOfConstraint Dirichlet;}
- If( Flag_Circ )
- {NameOfCoef Circ; EntityType GroupsOfNodesOf;
- NameOfConstraint DeltaPhi;}
- Else
- If( Flag_Object == 0 ) // if Cylinder only
- // In case of the Airfoil, the contraint on Dmdt is omitted
- // and replaced by an equation "Dmdt=$newDmdt"
- // See the "Resolution" section.
- {NameOfCoef Dmdt; EntityType GroupsOfNodesOf;
- NameOfConstraint MassFlowRate;}
- EndIf
- EndIf
- }
- }
-}
-
-Formulation{
- {Name PotentialFlow; Type FemEquation;
- Quantity{
- {Name phi; Type Local; NameOfSpace Vh;}
- { Name phiCont ; Type Local ; NameOfSpace Vh[phiCont] ; }
- { Name phiDisc ; Type Local ; NameOfSpace Vh[phiDisc] ; }
- { Name Circ ; Type Global ; NameOfSpace Vh[Circ] ; }
- { Name Dmdt ; Type Global ; NameOfSpace Vh[Dmdt] ; }
- }
- Equation{
- Galerkin{[ rho[] * Dof{d phi}, {d phi}];
- In Vol_rho; Jacobian Vol; Integration Int;}
- If( !Flag_Circ )
- GlobalTerm { [ -Dof{Dmdt} , {Circ} ] ; In Sur_Cut ; }
- If( Flag_Object == 1 )
- GlobalTerm { [ -Dof{Dmdt} , {Dmdt} ] ; In Sur_Cut ; }
- GlobalTerm { [ $newDmdt , {Dmdt} ] ; In Sur_Cut ; }
- EndIf
- EndIf
- }
- }
-}
-
-Resolution{
- {Name PotentialFlow;
- System{
- {Name A; NameOfFormulation PotentialFlow;}
- }
- Operation{
- InitSolution[A];
-
- If( Flag_Circ || ( Flag_Object == 0 ) )
-
- Generate[A]; Solve[A]; SaveSolution[A];
- PostOperation[Trailing];
-
- Else
- // A resolution can contain elementary algorithms.
- // Available commands are:
- // Evaluate[] : affectation of a run-time variable
- // Test[]{}{} : logical test
- // While[]{} : iteration
- // Print[{}, Format ..., File ...] : formatted display
-
- // A pseudo-Newton iteration is implemented here
- // to determine the value of Dmdt (in the Airfoil case)
- // that verifies Kutta's condition.
- // The run-time variable $newDmdt is used in Generate[A]
- // whereas $circ, $dmdt, $argV and $phiTrailing are evaluated
- // by the PostOperation[Trailing].
-
- DeleteFile["KJiter.txt"];
-
- Evaluate[$newDmdt = MassFlowRate];
- Evaluate[ $syscount = 0 ];
- Generate[A]; Solve[A]; SaveSolution[A];
-
- Evaluate[$dmdtp = MassFlowRate];
- Evaluate[$argVp = DeltaPhi];
- PostOperation[Trailing];
-
- Print[{$syscount, $circ, $dmdt, $argV},
- Format "iter = %3g Circ = %5.2f Dmdt = %5.2f argV = %5.2e"];
-
- While[ Norm[ $argV ] > 1e-3 && $syscount < 50] {
- Test[ $syscount && Norm[$argV-$argVp] > 1e-3 ]
- {Evaluate[$jac = Min[ ($dmdt-$dmdtp)/($argV-$argVp), 0.2 ] ] ;}
- {Evaluate[$jac = 0.2];}
-
- Evaluate[$newDmdt = $dmdt - $jac * $argV];
- Evaluate[ $syscount = $syscount + 1 ];
- Generate[A]; Solve[A]; SaveSolution[A];
-
- Evaluate[$dmdtp = $dmdt];
- Evaluate[$argVp = $argV];
- PostOperation[Trailing];
-
- Print[{$syscount, $circ, $dmdt, $jac, $argV},
- Format "iter = %3g Circ = %5.2f Dmdt = %5.2f jac=%5.2f argV = %5.3e"];
- }
- EndIf
- }
- }
-}
-
-PostProcessing{
- {Name PotentialFlow; NameOfFormulation PotentialFlow;
- Quantity{
- {Name phi; Value {
- Local{ [ {phi} ] ; In Dom_Vh; Jacobian Vol; } } }
- { Name phiCont ; Value {
- Local { [ { phiCont } ] ; In Dom_Vh ; Jacobian Vol ; } } }
- { Name phiDisc ; Value {
- Local { [ { phiDisc } ] ; In Dom_Vh ; Jacobian Vol ; } } }
- {Name velocity; Value {
- Local { [ {d phi} ]; In Dom_Vh; Jacobian Vol; } } }
- {Name normVelocity; Value {
- Local { [ Norm[{d phi}] ]; In Dom_Vh; Jacobian Vol; } } }
- {Name pressure; Value {
- Local { [-0.5*rho[]*SquNorm[ {d phi} ]];
- In Dom_Vh; Jacobian Vol; } } }
- {Name Angle; Value {
- Local{ [ argVTrail[{d phi}] ];
- In Dom_Vh; Jacobian Vol; } } }
-
- { Name Circ; Value { Local { [ {Circ} ]; In Sur_Cut; } } }
-
- { Name Dmdt; Value { Local { [ {Dmdt} ]; In Sur_Cut; } } }
-
- // Kutta-Jukowski approximation for Lift
- { Name LiftKJ; Value { Local { [ -rho[]*{Circ}*Velocity ];
- In Sur_Cut; } } }
-
- // Lift computed with the real pressure field
- { Name Lift;
- Value {
- Integral { [ -0.5*rho[]*SquNorm[{d phi}]*CompY[Normal[]] ];
- In Dom_Vh ; Jacobian Sur ; Integration Int; }
- }
- }
-
- { Name circulation;
- Value {
- Integral { [ {d phi} * Tangent[] ] ;
- In Dom_Vh ; Jacobian Sur ; Integration Int; }
- }
- }
-
- }
- }
-}
-
-PostOperation{
- {Name PotentialFlow; NameOfPostProcessing PotentialFlow;
- Operation{
-
- Print[Circ, OnRegion Sur_Cut, File > "output.txt", Color "Ivory",
- Format Table, SendToServer "Output/Circ" ];
-
- Print[Dmdt, OnRegion Sur_Cut, File > "output.txt", Color "Ivory",
- Format Table, SendToServer "Output/Dmdt" ];
-
- Print[LiftKJ, OnRegion Sur_Cut, File > "output.txt", Color "Ivory",
- Format Table, SendToServer "Output/LiftKJ" ];
-
- Print[Lift[GammaAirf], OnGlobal, Format Table,
- File > "output.txt", Color "Ivory",
- SendToServer "Output/Lift"];
-
- // Uncomment these lines to have more color maps
- //Print[phi, OnElementsOf Vol_rho, File "phi.pos"];
- //Print[phiDisc, OnElementsOf Vol_rho, File "phiDisc.pos"];
- //Print[phiCont, OnElementsOf Vol_rho, File "phiCont.pos"];
- //Print[pressure, OnElementsOf Vol_rho, File "p.pos"];
-
- Print[ velocity, OnElementsOf Vol_rho, File "velocity.pos"];
- Echo[ Str["l=PostProcessing.NbViews-1;",
- "View[l].VectorType = 1;",
- "View[l].LineWidth = 2;",
- "View[l].ArrowSizeMax = 100;",
- "View[l].CenterGlyphs = 1;"],
- File "tmp.geo", LastTimeStepOnly] ;
-
- // Stagnation points are points where Norm[{d phi}] is zero
- // This is better seen in log scale.
- Print[normVelocity, OnElementsOf Vol_rho, File "p.pos"];
- Echo[Str["l=PostProcessing.NbViews-1;",
- "View[l].Name = 'stagnation points';",
- "View[l].ScaleType = 2; // log scale"],
- File "tmp.geo"] ;
-
- If( Flag_Object == 0 )
- Print[phi, OnElementsOf Vol_rho, File "phi.pos"];
- Else
- // Show the isovalue "phi=$PhiTrailing"
- // which is perpendicular to the airfoil
- // iff the Kutta condition is fulfilled
- Print[phi, OnElementsOf Vol_rho, File "KJ.pos"];
- Print[{$phiTrailing, 1.001*$phiTrailing}, Format
- Str["l=PostProcessing.NbViews-1;",
- "View[l].Name = 'isovalue phiTrailing';",
- "View[l].IntervalsType = 3;",
- "Mesh.SurfaceEdges = 0; // hide mesh",
- "View[l].RangeType = 2; // custom range",
- "View[l].CustomMin = %g;",
- "View[l].CustomMax = %g;"],
- File "tmp.geo"] ;
- EndIf
- }
- }
-}
-
-PostOperation{ // for the Airfoil model
- {Name Trailing; NameOfPostProcessing PotentialFlow;
- Operation{
- Print[Circ, OnRegion Sur_Cut, File > "KJiter.txt", Format Table,
- StoreInVariable $circ,
- SendToServer "Output/Circ" ];
- Print[Dmdt, OnRegion Sur_Cut, File > "KJiter.txt", Format Table,
- StoreInVariable $dmdt,
- SendToServer "Output/Dmdt" ];
- // P_edge = {1.0001,0,0}
- Print[phi, OnPoint {1.0001,0,0}, File > "KJiter.txt", Color "Ivory",
- StoreInVariable $phiTrailing,
- Format Table, SendToServer "Output/PhiTrailing"];
-
- Print[Angle, OnPoint{1.0001,0,0}, File > "KJiter.txt", Color "Ivory",
- StoreInVariable $argV,
- Format Table, SendToServer "Output/argVTrailing"];
- }
- }
-}
-
-DefineConstant[
- R_ = {"PotentialFlow", Name "GetDP/1ResolutionChoices", Visible 0},
- C_ = {"-solve -pos", Name "GetDP/9ComputeCommand", Visible 0},
- P_ = {"PotentialFlow", Name "GetDP/2PostOperationChoices", Visible 0}
-];
-
+/* -------------------------------------------------------------------
+ Tutorial 6 : Potential flow and Magnus effect
+
+ Features:
+ - Potential flow, irrotational flow
+ - Multivalued scalar field
+ - Lift and Magnus effect, stagnation points
+ - Run-time variables
+ - Elementary algorithms in the Resolution section
+ - Non-linear iteration to achieve Kutta's condition
+
+ To compute the solution in a terminal:
+ getdp magnus.pro -solve PotentialFlow -pos PotentialFlow
+ gmsh magnus.geo velocity.pos
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > magnus.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+/*
+ This model solves a 2D potential flow around a cylinder or a naca airfoil
+ placed in a uniform "V_infinity" flow. Potential flows are defined by
+
+ V = grad phi => curl V = 0
+
+ where the multivalued scalar potential "phi" presents a discontinuity of
+ magnitude "deltaPhi" across a cut "Sur_Cut". In consequence, the velocity
+ field "V" is curl-free over the wole domain of analysis "Vol_rho" but its
+ circulation over any closed curve circling around the object, a quantity
+ often noted "Gamma" in the literature, gives "deltaPhi" as a result. The
+ circulation of "V" over closed curves not circling around the object is zero.
+
+ In the GetDP model, the discontinuity "deltaPhi" [m^2/s] is defined as a
+ global quantity in the Functional space of "phi". The associated (dual)
+ global quantity is the mass flow density, noted "Dmdt", which has [kg/s] as a
+ unit.
+
+ Governing equations are
+
+ div ( rho[] grad phi ) = 0 in Vol_rho
+ rho[] grad phi . n = rho[] Vn = 0 on Sur_Neu
+
+ whereas the uniform velocity field "V_infinity" is imposed by means of
+ Dirichlet boundary conditions on the upstream and downstream surfaces
+ "GammaUp" and "GammaDown".
+
+ Momentum equation is decoupled in case of stationary potential flows. The
+ velocity filed can be solved first, and the pressure is obtained afterwards
+ by invoking Bernoulli's theorem:
+
+ p = -0.5 * rho[] * SquNorm [ {d phi} ]
+
+ The "Lift" force in "Y" direction is then evaluated either by integrating "p
+ * CompY[Normal[]]" over the contour of the object, or by the Kutta-Jukowski
+ theorem
+
+ Lift = - L_z rho[] V_infinity Gamma
+
+ which is a first order approximation of the former.
+
+ "Cylinder" case:
+
+ Either the circulation "deltaPhi" or the mass flow rate "Dmdt" can be
+ imposed, according to the "Flag_Circ" flag. The Lift is evaluated by both
+ the integration of pressure and the Kutta-Jukowski approximation.
+
+ "Airfoil" case:
+
+ - If "Flag_Circ == 1", the model works similar to the "Cylinder" case.
+
+ - If "Flag_Circ == 0", the mass flow rate is not directly imposed in this
+ case. It is determined so that the Kutta condition is verified. This
+ condition states that the actual value of "Dmdt" is the one for which the
+ stagnation point (singularity of the velocity field) is located at the
+ trailing edge of the airfoil,. This is true when the function
+
+ argVTrail[] = ( Atan2[CompY[$1], CompX[$1] ] - Incidence ) / deg ;
+
+ returns zero when evaluated for the velocity at a point "P_edge" close to
+ the trailing edge of the airfoil. A non linear iteration is thus done by
+ means of a pseudo-newton scheme, updating the value of the imposed "Dmdt"
+ until the norm of the residual
+
+ f(V) = argVTrail[ {d phi } ] OnPoint {1.0001,0,0}
+
+ comes below a fixed tolerance. */
+
+Include "magnus_common.pro";
+
+Group{
+ // Physical regions
+ Fluid = Region[ 2 ];
+ GammaUp = Region[ 10 ];
+ GammaDown = Region[ 11 ];
+ GammaAirf = Region[ 12 ];
+ GammaCut = Region[ 13 ];
+
+ // Abstract regions
+ Vol_rho = Region[ { Fluid } ];
+ Sur_Dir = Region[ { GammaUp, GammaDown } ];
+ Sur_Neu = Region[ { GammaAirf } ];
+ Sur_Cut = Region[ { GammaCut } ];
+}
+
+Function{
+ rho[] = 1.225; // kg/m^3
+ MassFlowRate[] = MassFlowRate; // kg/s
+ DeltaPhi[] = DeltaPhi; // m^2/s
+ argVTrail[] = ( Atan2[CompY[$1], CompX[$1] ] - Incidence ) / deg ;
+}
+
+Jacobian {
+ { Name Vol ;
+ Case {
+ { Region All ; Jacobian Vol ; }
+ }
+ }
+ { Name Sur ;
+ Case {
+ { Region All ; Jacobian Sur ; }
+ }
+ }
+}
+
+Integration {
+ { Name Int ;
+ Case {
+ { Type Gauss ;
+ Case {
+ { GeoElement Point ; NumberOfPoints 1 ; }
+ { GeoElement Line ; NumberOfPoints 4 ; }
+ { GeoElement Triangle ; NumberOfPoints 6 ; }
+ { GeoElement Quadrangle ; NumberOfPoints 7 ; }
+ { GeoElement Tetrahedron ; NumberOfPoints 15 ; }
+ { GeoElement Hexahedron ; NumberOfPoints 34 ; }
+ }
+ }
+ }
+ }
+}
+
+Constraint{
+ { Name Dirichlet; Type Assign;
+ Case{
+ // Boundary conditions for the V_infinity uniform flow
+ { Region GammaDown; Value Velocity*BoxSize; }
+ { Region GammaUp ; Value 0; }
+ }
+ }
+ { Name DeltaPhi; Type Assign;
+ Case{
+ { Region Sur_Cut; Value DeltaPhi[]; }
+ }
+ }
+ { Name MassFlowRate; Type Assign;
+ Case{
+ { Region Sur_Cut; Value MassFlowRate[]; }
+ }
+ }
+}
+
+// Domains of definition used in the description of the function space
+// These groups contain both volume and surface regions/elements.
+Group{
+ Dom_Vh = Region[ { Vol_rho, Sur_Dir, Sur_Neu, Sur_Cut } ];
+ Dom_Cut = ElementsOf[ Dom_Vh, OnPositiveSideOf Sur_Cut ];
+}
+FunctionSpace{
+ { Name Vh; Type Form0;
+ BasisFunction{
+ { Name vn; NameOfCoef phin; Function BF_Node;
+ Support Dom_Vh; Entity NodesOf[All]; }
+ { Name vc; NameOfCoef dphi; Function BF_GroupOfNodes;
+ Support Dom_Cut; Entity GroupsOfNodesOf[ Sur_Cut ];}
+ }
+ SubSpace {
+ { Name phiCont ; NameOfBasisFunction { vn } ; }
+ { Name phiDisc ; NameOfBasisFunction { vc } ; }
+ }
+ GlobalQuantity {
+ { Name Circ ; Type AliasOf ; NameOfCoef dphi ; }
+ { Name Dmdt ; Type AssociatedWith ; NameOfCoef dphi ; }
+ }
+ Constraint{
+ {NameOfCoef phin; EntityType NodesOf;
+ NameOfConstraint Dirichlet;}
+ If( Flag_Circ )
+ {NameOfCoef Circ; EntityType GroupsOfNodesOf;
+ NameOfConstraint DeltaPhi;}
+ Else
+ If( Flag_Object == 0 ) // if Cylinder only
+ // In case of the Airfoil, the contraint on Dmdt is omitted
+ // and replaced by an equation "Dmdt=$newDmdt"
+ // See the "Resolution" section.
+ {NameOfCoef Dmdt; EntityType GroupsOfNodesOf;
+ NameOfConstraint MassFlowRate;}
+ EndIf
+ EndIf
+ }
+ }
+}
+
+Formulation{
+ {Name PotentialFlow; Type FemEquation;
+ Quantity{
+ {Name phi; Type Local; NameOfSpace Vh;}
+ { Name phiCont ; Type Local ; NameOfSpace Vh[phiCont] ; }
+ { Name phiDisc ; Type Local ; NameOfSpace Vh[phiDisc] ; }
+ { Name Circ ; Type Global ; NameOfSpace Vh[Circ] ; }
+ { Name Dmdt ; Type Global ; NameOfSpace Vh[Dmdt] ; }
+ }
+ Equation{
+ Integral{[ rho[] * Dof{d phi}, {d phi}];
+ In Vol_rho; Jacobian Vol; Integration Int;}
+ If( !Flag_Circ )
+ GlobalTerm { [ -Dof{Dmdt} , {Circ} ] ; In Sur_Cut ; }
+ If( Flag_Object == 1 )
+ GlobalTerm { [ -Dof{Dmdt} , {Dmdt} ] ; In Sur_Cut ; }
+ GlobalTerm { [ $newDmdt , {Dmdt} ] ; In Sur_Cut ; }
+ EndIf
+ EndIf
+ }
+ }
+}
+
+Resolution{
+ {Name PotentialFlow;
+ System{
+ {Name A; NameOfFormulation PotentialFlow;}
+ }
+ Operation{
+ InitSolution[A];
+
+ If( Flag_Circ || ( Flag_Object == 0 ) )
+
+ Generate[A]; Solve[A]; SaveSolution[A];
+ PostOperation[Trailing];
+
+ Else
+ // A resolution can contain elementary algorithms.
+ // Available commands are:
+ // Evaluate[] : affectation of a run-time variable
+ // Test[]{}{} : logical test
+ // While[]{} : iteration
+ // Print[{}, Format ..., File ...] : formatted display
+
+ // A pseudo-Newton iteration is implemented here
+ // to determine the value of Dmdt (in the Airfoil case)
+ // that verifies Kutta's condition.
+ // The run-time variable $newDmdt is used in Generate[A]
+ // whereas $circ, $dmdt, $argV and $phiTrailing are evaluated
+ // by the PostOperation[Trailing].
+
+ DeleteFile["KJiter.txt"];
+
+ Evaluate[$newDmdt = MassFlowRate];
+ Evaluate[ $syscount = 0 ];
+ Generate[A]; Solve[A]; SaveSolution[A];
+
+ Evaluate[$dmdtp = MassFlowRate];
+ Evaluate[$argVp = DeltaPhi];
+ PostOperation[Trailing];
+
+ Print[{$syscount, $circ, $dmdt, $argV},
+ Format "iter = %3g Circ = %5.2f Dmdt = %5.2f argV = %5.2e"];
+
+ While[ Norm[ $argV ] > 1e-3 && $syscount < 50] {
+ Test[ $syscount && Norm[$argV-$argVp] > 1e-3 ]
+ {Evaluate[$jac = Min[ ($dmdt-$dmdtp)/($argV-$argVp), 0.2 ] ] ;}
+ {Evaluate[$jac = 0.2];}
+
+ Evaluate[$newDmdt = $dmdt - $jac * $argV];
+ Evaluate[ $syscount = $syscount + 1 ];
+ Generate[A]; Solve[A]; SaveSolution[A];
+
+ Evaluate[$dmdtp = $dmdt];
+ Evaluate[$argVp = $argV];
+ PostOperation[Trailing];
+
+ Print[{$syscount, $circ, $dmdt, $jac, $argV},
+ Format "iter = %3g Circ = %5.2f Dmdt = %5.2f jac=%5.2f argV = %5.3e"];
+ }
+ EndIf
+ }
+ }
+}
+
+PostProcessing{
+ {Name PotentialFlow; NameOfFormulation PotentialFlow;
+ Quantity{
+ {Name phi; Value {
+ Local{ [ {phi} ] ; In Dom_Vh; Jacobian Vol; } } }
+ { Name phiCont ; Value {
+ Local { [ { phiCont } ] ; In Dom_Vh ; Jacobian Vol ; } } }
+ { Name phiDisc ; Value {
+ Local { [ { phiDisc } ] ; In Dom_Vh ; Jacobian Vol ; } } }
+ {Name velocity; Value {
+ Local { [ {d phi} ]; In Dom_Vh; Jacobian Vol; } } }
+ {Name normVelocity; Value {
+ Local { [ Norm[{d phi}] ]; In Dom_Vh; Jacobian Vol; } } }
+ {Name pressure; Value {
+ Local { [-0.5*rho[]*SquNorm[ {d phi} ]];
+ In Dom_Vh; Jacobian Vol; } } }
+ {Name Angle; Value {
+ Local{ [ argVTrail[{d phi}] ];
+ In Dom_Vh; Jacobian Vol; } } }
+
+ { Name Circ; Value { Local { [ {Circ} ]; In Sur_Cut; } } }
+
+ { Name Dmdt; Value { Local { [ {Dmdt} ]; In Sur_Cut; } } }
+
+ // Kutta-Jukowski approximation for Lift
+ { Name LiftKJ; Value { Local { [ -rho[]*{Circ}*Velocity ];
+ In Sur_Cut; } } }
+
+ // Lift computed with the real pressure field
+ { Name Lift;
+ Value {
+ Integral { [ -0.5*rho[]*SquNorm[{d phi}]*CompY[Normal[]] ];
+ In Dom_Vh ; Jacobian Sur ; Integration Int; }
+ }
+ }
+
+ { Name circulation;
+ Value {
+ Integral { [ {d phi} * Tangent[] ] ;
+ In Dom_Vh ; Jacobian Sur ; Integration Int; }
+ }
+ }
+
+ }
+ }
+}
+
+PostOperation{
+ {Name PotentialFlow; NameOfPostProcessing PotentialFlow;
+ Operation{
+
+ Print[Circ, OnRegion Sur_Cut, File > "output.txt", Color "Ivory",
+ Format Table, SendToServer "Output/Circ" ];
+
+ Print[Dmdt, OnRegion Sur_Cut, File > "output.txt", Color "Ivory",
+ Format Table, SendToServer "Output/Dmdt" ];
+
+ Print[LiftKJ, OnRegion Sur_Cut, File > "output.txt", Color "Ivory",
+ Format Table, SendToServer "Output/LiftKJ" ];
+
+ Print[Lift[GammaAirf], OnGlobal, Format Table,
+ File > "output.txt", Color "Ivory",
+ SendToServer "Output/Lift"];
+
+ // Uncomment these lines to have more color maps
+ //Print[phi, OnElementsOf Vol_rho, File "phi.pos"];
+ //Print[phiDisc, OnElementsOf Vol_rho, File "phiDisc.pos"];
+ //Print[phiCont, OnElementsOf Vol_rho, File "phiCont.pos"];
+ //Print[pressure, OnElementsOf Vol_rho, File "p.pos"];
+
+ Print[ velocity, OnElementsOf Vol_rho, File "velocity.pos"];
+ Echo[ Str["l=PostProcessing.NbViews-1;",
+ "View[l].VectorType = 1;",
+ "View[l].LineWidth = 2;",
+ "View[l].ArrowSizeMax = 100;",
+ "View[l].CenterGlyphs = 1;"],
+ File "tmp.geo", LastTimeStepOnly] ;
+
+ // Stagnation points are points where Norm[{d phi}] is zero
+ // This is better seen in log scale.
+ Print[normVelocity, OnElementsOf Vol_rho, File "p.pos"];
+ Echo[Str["l=PostProcessing.NbViews-1;",
+ "View[l].Name = 'stagnation points';",
+ "View[l].ScaleType = 2; // log scale"],
+ File "tmp.geo"] ;
+
+ If( Flag_Object == 0 )
+ Print[phi, OnElementsOf Vol_rho, File "phi.pos"];
+ Else
+ // Show the isovalue "phi=$PhiTrailing"
+ // which is perpendicular to the airfoil
+ // iff the Kutta condition is fulfilled
+ Print[phi, OnElementsOf Vol_rho, File "KJ.pos"];
+ Print[{$phiTrailing, 1.001*$phiTrailing}, Format
+ Str["l=PostProcessing.NbViews-1;",
+ "View[l].Name = 'isovalue phiTrailing';",
+ "View[l].IntervalsType = 3;",
+ "Mesh.SurfaceEdges = 0; // hide mesh",
+ "View[l].RangeType = 2; // custom range",
+ "View[l].CustomMin = %g;",
+ "View[l].CustomMax = %g;"],
+ File "tmp.geo"] ;
+ EndIf
+ }
+ }
+}
+
+PostOperation{ // for the Airfoil model
+ {Name Trailing; NameOfPostProcessing PotentialFlow;
+ Operation{
+ Print[Circ, OnRegion Sur_Cut, File > "KJiter.txt", Format Table,
+ StoreInVariable $circ,
+ SendToServer "Output/Circ" ];
+ Print[Dmdt, OnRegion Sur_Cut, File > "KJiter.txt", Format Table,
+ StoreInVariable $dmdt,
+ SendToServer "Output/Dmdt" ];
+ // P_edge = {1.0001,0,0}
+ Print[phi, OnPoint {1.0001,0,0}, File > "KJiter.txt", Color "Ivory",
+ StoreInVariable $phiTrailing,
+ Format Table, SendToServer "Output/PhiTrailing"];
+
+ Print[Angle, OnPoint{1.0001,0,0}, File > "KJiter.txt", Color "Ivory",
+ StoreInVariable $argV,
+ Format Table, SendToServer "Output/argVTrailing"];
+ }
+ }
+}
+
+DefineConstant[
+ R_ = {"PotentialFlow", Name "GetDP/1ResolutionChoices", Visible 0},
+ C_ = {"-solve -pos", Name "GetDP/9ComputeCommand", Visible 0},
+ P_ = {"PotentialFlow", Name "GetDP/2PostOperationChoices", Visible 0}
+];
diff --git a/PotentialFlow/magnus_common.pro b/PotentialFlow/magnus_common.pro
index b9c659b..f1c65c4 100644
--- a/PotentialFlow/magnus_common.pro
+++ b/PotentialFlow/magnus_common.pro
@@ -1,27 +1,27 @@
-cm = 1e-2;
-deg = Pi/180;
-kmh = 10./36.;
-
-Flag_Circ =
- DefineNumber[0, Name "Model/Impose circulation", Choices {0, 1} ];
-Flag_Object =
- DefineNumber[1, Name "Model/Object",
- Choices {0="Cylinder", 1="Airfoil"} ];
-
-BoxSize =
- DefineNumber[7, Name "Model/Air box size [m]", Help "In flow direction."];
-Velocity = kmh*
- DefineNumber[100, Name "Model/V", Label "Model/Flow velocity [km/h]"];
-Incidence = -deg*
- DefineNumber[10, Name "Model/Angle of attack [deg]", Visible Flag_Object];
-
-// Negative circulation for a positive lift.
-DeltaPhi = (-1)*
- DefineNumber[10, Name "Model/Circ", Visible Flag_Circ,
- Min 0, Max 20, Step 2,
- Label "Circulation around foil [m^2/s]"];
-
-MassFlowRate =
- DefineNumber[-100, Name "Model/Dmdt", Visible !Flag_Circ,
- Label "Mass flow rate [kg/s]"];
-
+cm = 1e-2;
+deg = Pi/180;
+kmh = 10./36.;
+
+Flag_Circ =
+ DefineNumber[0, Name "Model/Impose circulation", Choices {0, 1} ];
+Flag_Object =
+ DefineNumber[1, Name "Model/Object",
+ Choices {0="Cylinder", 1="Airfoil"} ];
+
+BoxSize =
+ DefineNumber[7, Name "Model/Air box size [m]", Help "In flow direction."];
+Velocity = kmh*
+ DefineNumber[100, Name "Model/V", Label "Model/Flow velocity [km/h]"];
+Incidence = -deg*
+ DefineNumber[10, Name "Model/Angle of attack [deg]", Visible Flag_Object];
+
+// Negative circulation for a positive lift.
+DeltaPhi = (-1)*
+ DefineNumber[10, Name "Model/Circ", Visible Flag_Circ,
+ Min 0, Max 20, Step 2,
+ Label "Circulation around foil [m^2/s]"];
+
+MassFlowRate =
+ DefineNumber[-100, Name "Model/Dmdt", Visible !Flag_Circ,
+ Label "Mass flow rate [kg/s]"];
+
diff --git a/PotentialFlow/nacaAirfoil.geo b/PotentialFlow/nacaAirfoil.geo
index 9ef6199..764a17d 100644
--- a/PotentialFlow/nacaAirfoil.geo
+++ b/PotentialFlow/nacaAirfoil.geo
@@ -1,222 +1,222 @@
-
-
-Point(1) = {1.000000,0.000000,0,lca};
-Point(2) = {0.999753,-0.000035,0,lca};
-Point(3) = {0.999013,-0.000141,0,lca};
-Point(4) = {0.997781,-0.000317,0,lca};
-Point(5) = {0.996057,-0.000562,0,lca};
-Point(6) = {0.993844,-0.000876,0,lca};
-Point(7) = {0.991144,-0.001258,0,lca};
-Point(8) = {0.987958,-0.001707,0,lca};
-Point(9) = {0.984292,-0.002222,0,lca};
-Point(10) = {0.980147,-0.002801,0,lca};
-Point(11) = {0.975528,-0.003443,0,lca};
-Point(12) = {0.970440,-0.004147,0,lca};
-Point(13) = {0.964888,-0.004909,0,lca};
-Point(14) = {0.958877,-0.005729,0,lca};
-Point(15) = {0.952414,-0.006603,0,lca};
-Point(16) = {0.945503,-0.007531,0,lca};
-Point(17) = {0.938153,-0.008510,0,lca};
-Point(18) = {0.930371,-0.009537,0,lca};
-Point(19) = {0.922164,-0.010610,0,lca};
-Point(20) = {0.913540,-0.011726,0,lca};
-Point(21) = {0.904508,-0.012883,0,lca};
-Point(22) = {0.895078,-0.014079,0,lca};
-Point(23) = {0.885257,-0.015310,0,lca};
-Point(24) = {0.875056,-0.016574,0,lca};
-Point(25) = {0.864484,-0.017868,0,lca};
-Point(26) = {0.853553,-0.019189,0,lca};
-Point(27) = {0.842274,-0.020535,0,lca};
-Point(28) = {0.830656,-0.021904,0,lca};
-Point(29) = {0.818712,-0.023291,0,lca};
-Point(30) = {0.806454,-0.024694,0,lca};
-Point(31) = {0.793893,-0.026111,0,lca};
-Point(32) = {0.781042,-0.027539,0,lca};
-Point(33) = {0.767913,-0.028974,0,lca};
-Point(34) = {0.754521,-0.030414,0,lca};
-Point(35) = {0.740877,-0.031856,0,lca};
-Point(36) = {0.726995,-0.033296,0,lca};
-Point(37) = {0.712890,-0.034733,0,lca};
-Point(38) = {0.698574,-0.036163,0,lca};
-Point(39) = {0.684062,-0.037582,0,lca};
-Point(40) = {0.669369,-0.038988,0,lca};
-Point(41) = {0.654508,-0.040378,0,lca};
-Point(42) = {0.639496,-0.041747,0,lca};
-Point(43) = {0.624345,-0.043094,0,lca};
-Point(44) = {0.609072,-0.044414,0,lca};
-Point(45) = {0.593691,-0.045705,0,lca};
-Point(46) = {0.578217,-0.046962,0,lca};
-Point(47) = {0.562667,-0.048182,0,lca};
-Point(48) = {0.547054,-0.049362,0,lca};
-Point(49) = {0.531395,-0.050499,0,lca};
-Point(50) = {0.515705,-0.051587,0,lca};
-Point(51) = {0.500000,-0.052625,0,lca};
-Point(52) = {0.484295,-0.053608,0,lca};
-Point(53) = {0.468605,-0.054534,0,lca};
-Point(54) = {0.452946,-0.055397,0,lca};
-Point(55) = {0.437333,-0.056195,0,lca};
-Point(56) = {0.421783,-0.056924,0,lca};
-Point(57) = {0.406309,-0.057581,0,lca};
-Point(58) = {0.390928,-0.058163,0,lca};
-Point(59) = {0.375655,-0.058666,0,lca};
-Point(60) = {0.360504,-0.059087,0,lca};
-Point(61) = {0.345492,-0.059424,0,lca};
-Point(62) = {0.330631,-0.059674,0,lca};
-Point(63) = {0.315938,-0.059834,0,lca};
-Point(64) = {0.301426,-0.059902,0,lca};
-Point(65) = {0.287110,-0.059876,0,lca};
-Point(66) = {0.273005,-0.059754,0,lca};
-Point(67) = {0.259123,-0.059535,0,lca};
-Point(68) = {0.245479,-0.059217,0,lca};
-Point(69) = {0.232087,-0.058799,0,lca};
-Point(70) = {0.218958,-0.058280,0,lca};
-Point(71) = {0.206107,-0.057661,0,lca};
-Point(72) = {0.193546,-0.056940,0,lca};
-Point(73) = {0.181288,-0.056119,0,lca};
-Point(74) = {0.169344,-0.055197,0,lca};
-Point(75) = {0.157726,-0.054176,0,lca};
-Point(76) = {0.146447,-0.053056,0,lca};
-Point(77) = {0.135516,-0.051839,0,lca};
-Point(78) = {0.124944,-0.050527,0,lca};
-Point(79) = {0.114743,-0.049121,0,lca};
-Point(80) = {0.104922,-0.047624,0,lca};
-Point(81) = {0.095492,-0.046037,0,lca};
-Point(82) = {0.086460,-0.044364,0,lca};
-Point(83) = {0.077836,-0.042608,0,lca};
-Point(84) = {0.069629,-0.040770,0,lca};
-Point(85) = {0.061847,-0.038854,0,lca};
-Point(86) = {0.054497,-0.036863,0,lca};
-Point(87) = {0.047586,-0.034800,0,lca};
-Point(88) = {0.041123,-0.032668,0,lca};
-Point(89) = {0.035112,-0.030471,0,lca};
-Point(90) = {0.029560,-0.028212,0,lca};
-Point(91) = {0.024472,-0.025893,0,lca};
-Point(92) = {0.019853,-0.023517,0,lca};
-Point(93) = {0.015708,-0.021088,0,lca};
-Point(94) = {0.012042,-0.018607,0,lca};
-Point(95) = {0.008856,-0.016078,0,lca};
-Point(96) = {0.006156,-0.013503,0,lca};
-Point(97) = {0.003943,-0.010884,0,lca};
-Point(98) = {0.002219,-0.008223,0,lca};
-Point(99) = {0.000987,-0.005521,0,lca};
-Point(100) = {0.000247,-0.002779,0,lca};
-Point(101) = {0.000000,0.000000,0,lca};
-Point(102) = {0.000247,0.002779,0,lca};
-Point(103) = {0.000987,0.005521,0,lca};
-Point(104) = {0.002219,0.008223,0,lca};
-Point(105) = {0.003943,0.010884,0,lca};
-Point(106) = {0.006156,0.013503,0,lca};
-Point(107) = {0.008856,0.016078,0,lca};
-Point(108) = {0.012042,0.018607,0,lca};
-Point(109) = {0.015708,0.021088,0,lca};
-Point(110) = {0.019853,0.023517,0,lca};
-Point(111) = {0.024472,0.025893,0,lca};
-Point(112) = {0.029560,0.028212,0,lca};
-Point(113) = {0.035112,0.030471,0,lca};
-Point(114) = {0.041123,0.032668,0,lca};
-Point(115) = {0.047586,0.034800,0,lca};
-Point(116) = {0.054497,0.036863,0,lca};
-Point(117) = {0.061847,0.038854,0,lca};
-Point(118) = {0.069629,0.040770,0,lca};
-Point(119) = {0.077836,0.042608,0,lca};
-Point(120) = {0.086460,0.044364,0,lca};
-Point(121) = {0.095492,0.046037,0,lca};
-Point(122) = {0.104922,0.047624,0,lca};
-Point(123) = {0.114743,0.049121,0,lca};
-Point(124) = {0.124944,0.050527,0,lca};
-Point(125) = {0.135516,0.051839,0,lca};
-Point(126) = {0.146447,0.053056,0,lca};
-Point(127) = {0.157726,0.054176,0,lca};
-Point(128) = {0.169344,0.055197,0,lca};
-Point(129) = {0.181288,0.056119,0,lca};
-Point(130) = {0.193546,0.056940,0,lca};
-Point(131) = {0.206107,0.057661,0,lca};
-Point(132) = {0.218958,0.058280,0,lca};
-Point(133) = {0.232087,0.058799,0,lca};
-Point(134) = {0.245479,0.059217,0,lca};
-Point(135) = {0.259123,0.059535,0,lca};
-Point(136) = {0.273005,0.059754,0,lca};
-Point(137) = {0.287110,0.059876,0,lca};
-Point(138) = {0.301426,0.059902,0,lca};
-Point(139) = {0.315938,0.059834,0,lca};
-Point(140) = {0.330631,0.059674,0,lca};
-Point(141) = {0.345492,0.059424,0,lca};
-Point(142) = {0.360504,0.059087,0,lca};
-Point(143) = {0.375655,0.058666,0,lca};
-Point(144) = {0.390928,0.058163,0,lca};
-Point(145) = {0.406309,0.057581,0,lca};
-Point(146) = {0.421783,0.056924,0,lca};
-Point(147) = {0.437333,0.056195,0,lca};
-Point(148) = {0.452946,0.055397,0,lca};
-Point(149) = {0.468605,0.054534,0,lca};
-Point(150) = {0.484295,0.053608,0,lca};
-Point(151) = {0.500000,0.052625,0,lca};
-Point(152) = {0.515705,0.051587,0,lca};
-Point(153) = {0.531395,0.050499,0,lca};
-Point(154) = {0.547054,0.049362,0,lca};
-Point(155) = {0.562667,0.048182,0,lca};
-Point(156) = {0.578217,0.046962,0,lca};
-Point(157) = {0.593691,0.045705,0,lca};
-Point(158) = {0.609072,0.044414,0,lca};
-Point(159) = {0.624345,0.043094,0,lca};
-Point(160) = {0.639496,0.041747,0,lca};
-Point(161) = {0.654508,0.040378,0,lca};
-Point(162) = {0.669369,0.038988,0,lca};
-Point(163) = {0.684062,0.037582,0,lca};
-Point(164) = {0.698574,0.036163,0,lca};
-Point(165) = {0.712890,0.034733,0,lca};
-Point(166) = {0.726995,0.033296,0,lca};
-Point(167) = {0.740877,0.031856,0,lca};
-Point(168) = {0.754521,0.030414,0,lca};
-Point(169) = {0.767913,0.028974,0,lca};
-Point(170) = {0.781042,0.027539,0,lca};
-Point(171) = {0.793893,0.026111,0,lca};
-Point(172) = {0.806454,0.024694,0,lca};
-Point(173) = {0.818712,0.023291,0,lca};
-Point(174) = {0.830656,0.021904,0,lca};
-Point(175) = {0.842274,0.020535,0,lca};
-Point(176) = {0.853553,0.019189,0,lca};
-Point(177) = {0.864484,0.017868,0,lca};
-Point(178) = {0.875056,0.016574,0,lca};
-Point(179) = {0.885257,0.015310,0,lca};
-Point(180) = {0.895078,0.014079,0,lca};
-Point(181) = {0.904508,0.012883,0,lca};
-Point(182) = {0.913540,0.011726,0,lca};
-Point(183) = {0.922164,0.010610,0,lca};
-Point(184) = {0.930371,0.009537,0,lca};
-Point(185) = {0.938153,0.008510,0,lca};
-Point(186) = {0.945503,0.007531,0,lca};
-Point(187) = {0.952414,0.006603,0,lca};
-Point(188) = {0.958877,0.005729,0,lca};
-Point(189) = {0.964888,0.004909,0,lca};
-Point(190) = {0.970440,0.004147,0,lca};
-Point(191) = {0.975528,0.003443,0,lca};
-Point(192) = {0.980147,0.002801,0,lca};
-Point(193) = {0.984292,0.002222,0,lca};
-Point(194) = {0.987958,0.001707,0,lca};
-Point(195) = {0.991144,0.001258,0,lca};
-Point(196) = {0.993844,0.000876,0,lca};
-Point(197) = {0.996057,0.000562,0,lca};
-Point(198) = {0.997781,0.000317,0,lca};
-Point(199) = {0.999013,0.000141,0,lca};
-Point(200) = {0.999753,0.000035,0,lca};
-
-//Points numerotation:
-numberLeadingEgde = 101 ;
-numberLowerSurface = 81 ;
-numberUpperSurface = 121 ;
-
-//Distances:
-distanceTrailingLowerPoint = 0.908262 ;
-distanceLowerUpperPoint = 0.222905 ;
-distanceUpperTrailingPoint = 0.908262 ;
-
-Line(1) = { 1 ... 81 };
-Line(2) = { 81 ... 101 };
-Line(3) = { 101 ... 121 };
-Line(4) = { 121 ... 200, 1 };
-
-Rotate { {0,0,1}, {1,0,0}, Incidence } { Line { 1 ... 4 } ; }
-
-/* Line Loop(1) = {1,2,3,4}; */
-/* Plane Surface(1) = {1}; */
+
+
+Point(1) = {1.000000,0.000000,0,lca};
+Point(2) = {0.999753,-0.000035,0,lca};
+Point(3) = {0.999013,-0.000141,0,lca};
+Point(4) = {0.997781,-0.000317,0,lca};
+Point(5) = {0.996057,-0.000562,0,lca};
+Point(6) = {0.993844,-0.000876,0,lca};
+Point(7) = {0.991144,-0.001258,0,lca};
+Point(8) = {0.987958,-0.001707,0,lca};
+Point(9) = {0.984292,-0.002222,0,lca};
+Point(10) = {0.980147,-0.002801,0,lca};
+Point(11) = {0.975528,-0.003443,0,lca};
+Point(12) = {0.970440,-0.004147,0,lca};
+Point(13) = {0.964888,-0.004909,0,lca};
+Point(14) = {0.958877,-0.005729,0,lca};
+Point(15) = {0.952414,-0.006603,0,lca};
+Point(16) = {0.945503,-0.007531,0,lca};
+Point(17) = {0.938153,-0.008510,0,lca};
+Point(18) = {0.930371,-0.009537,0,lca};
+Point(19) = {0.922164,-0.010610,0,lca};
+Point(20) = {0.913540,-0.011726,0,lca};
+Point(21) = {0.904508,-0.012883,0,lca};
+Point(22) = {0.895078,-0.014079,0,lca};
+Point(23) = {0.885257,-0.015310,0,lca};
+Point(24) = {0.875056,-0.016574,0,lca};
+Point(25) = {0.864484,-0.017868,0,lca};
+Point(26) = {0.853553,-0.019189,0,lca};
+Point(27) = {0.842274,-0.020535,0,lca};
+Point(28) = {0.830656,-0.021904,0,lca};
+Point(29) = {0.818712,-0.023291,0,lca};
+Point(30) = {0.806454,-0.024694,0,lca};
+Point(31) = {0.793893,-0.026111,0,lca};
+Point(32) = {0.781042,-0.027539,0,lca};
+Point(33) = {0.767913,-0.028974,0,lca};
+Point(34) = {0.754521,-0.030414,0,lca};
+Point(35) = {0.740877,-0.031856,0,lca};
+Point(36) = {0.726995,-0.033296,0,lca};
+Point(37) = {0.712890,-0.034733,0,lca};
+Point(38) = {0.698574,-0.036163,0,lca};
+Point(39) = {0.684062,-0.037582,0,lca};
+Point(40) = {0.669369,-0.038988,0,lca};
+Point(41) = {0.654508,-0.040378,0,lca};
+Point(42) = {0.639496,-0.041747,0,lca};
+Point(43) = {0.624345,-0.043094,0,lca};
+Point(44) = {0.609072,-0.044414,0,lca};
+Point(45) = {0.593691,-0.045705,0,lca};
+Point(46) = {0.578217,-0.046962,0,lca};
+Point(47) = {0.562667,-0.048182,0,lca};
+Point(48) = {0.547054,-0.049362,0,lca};
+Point(49) = {0.531395,-0.050499,0,lca};
+Point(50) = {0.515705,-0.051587,0,lca};
+Point(51) = {0.500000,-0.052625,0,lca};
+Point(52) = {0.484295,-0.053608,0,lca};
+Point(53) = {0.468605,-0.054534,0,lca};
+Point(54) = {0.452946,-0.055397,0,lca};
+Point(55) = {0.437333,-0.056195,0,lca};
+Point(56) = {0.421783,-0.056924,0,lca};
+Point(57) = {0.406309,-0.057581,0,lca};
+Point(58) = {0.390928,-0.058163,0,lca};
+Point(59) = {0.375655,-0.058666,0,lca};
+Point(60) = {0.360504,-0.059087,0,lca};
+Point(61) = {0.345492,-0.059424,0,lca};
+Point(62) = {0.330631,-0.059674,0,lca};
+Point(63) = {0.315938,-0.059834,0,lca};
+Point(64) = {0.301426,-0.059902,0,lca};
+Point(65) = {0.287110,-0.059876,0,lca};
+Point(66) = {0.273005,-0.059754,0,lca};
+Point(67) = {0.259123,-0.059535,0,lca};
+Point(68) = {0.245479,-0.059217,0,lca};
+Point(69) = {0.232087,-0.058799,0,lca};
+Point(70) = {0.218958,-0.058280,0,lca};
+Point(71) = {0.206107,-0.057661,0,lca};
+Point(72) = {0.193546,-0.056940,0,lca};
+Point(73) = {0.181288,-0.056119,0,lca};
+Point(74) = {0.169344,-0.055197,0,lca};
+Point(75) = {0.157726,-0.054176,0,lca};
+Point(76) = {0.146447,-0.053056,0,lca};
+Point(77) = {0.135516,-0.051839,0,lca};
+Point(78) = {0.124944,-0.050527,0,lca};
+Point(79) = {0.114743,-0.049121,0,lca};
+Point(80) = {0.104922,-0.047624,0,lca};
+Point(81) = {0.095492,-0.046037,0,lca};
+Point(82) = {0.086460,-0.044364,0,lca};
+Point(83) = {0.077836,-0.042608,0,lca};
+Point(84) = {0.069629,-0.040770,0,lca};
+Point(85) = {0.061847,-0.038854,0,lca};
+Point(86) = {0.054497,-0.036863,0,lca};
+Point(87) = {0.047586,-0.034800,0,lca};
+Point(88) = {0.041123,-0.032668,0,lca};
+Point(89) = {0.035112,-0.030471,0,lca};
+Point(90) = {0.029560,-0.028212,0,lca};
+Point(91) = {0.024472,-0.025893,0,lca};
+Point(92) = {0.019853,-0.023517,0,lca};
+Point(93) = {0.015708,-0.021088,0,lca};
+Point(94) = {0.012042,-0.018607,0,lca};
+Point(95) = {0.008856,-0.016078,0,lca};
+Point(96) = {0.006156,-0.013503,0,lca};
+Point(97) = {0.003943,-0.010884,0,lca};
+Point(98) = {0.002219,-0.008223,0,lca};
+Point(99) = {0.000987,-0.005521,0,lca};
+Point(100) = {0.000247,-0.002779,0,lca};
+Point(101) = {0.000000,0.000000,0,lca};
+Point(102) = {0.000247,0.002779,0,lca};
+Point(103) = {0.000987,0.005521,0,lca};
+Point(104) = {0.002219,0.008223,0,lca};
+Point(105) = {0.003943,0.010884,0,lca};
+Point(106) = {0.006156,0.013503,0,lca};
+Point(107) = {0.008856,0.016078,0,lca};
+Point(108) = {0.012042,0.018607,0,lca};
+Point(109) = {0.015708,0.021088,0,lca};
+Point(110) = {0.019853,0.023517,0,lca};
+Point(111) = {0.024472,0.025893,0,lca};
+Point(112) = {0.029560,0.028212,0,lca};
+Point(113) = {0.035112,0.030471,0,lca};
+Point(114) = {0.041123,0.032668,0,lca};
+Point(115) = {0.047586,0.034800,0,lca};
+Point(116) = {0.054497,0.036863,0,lca};
+Point(117) = {0.061847,0.038854,0,lca};
+Point(118) = {0.069629,0.040770,0,lca};
+Point(119) = {0.077836,0.042608,0,lca};
+Point(120) = {0.086460,0.044364,0,lca};
+Point(121) = {0.095492,0.046037,0,lca};
+Point(122) = {0.104922,0.047624,0,lca};
+Point(123) = {0.114743,0.049121,0,lca};
+Point(124) = {0.124944,0.050527,0,lca};
+Point(125) = {0.135516,0.051839,0,lca};
+Point(126) = {0.146447,0.053056,0,lca};
+Point(127) = {0.157726,0.054176,0,lca};
+Point(128) = {0.169344,0.055197,0,lca};
+Point(129) = {0.181288,0.056119,0,lca};
+Point(130) = {0.193546,0.056940,0,lca};
+Point(131) = {0.206107,0.057661,0,lca};
+Point(132) = {0.218958,0.058280,0,lca};
+Point(133) = {0.232087,0.058799,0,lca};
+Point(134) = {0.245479,0.059217,0,lca};
+Point(135) = {0.259123,0.059535,0,lca};
+Point(136) = {0.273005,0.059754,0,lca};
+Point(137) = {0.287110,0.059876,0,lca};
+Point(138) = {0.301426,0.059902,0,lca};
+Point(139) = {0.315938,0.059834,0,lca};
+Point(140) = {0.330631,0.059674,0,lca};
+Point(141) = {0.345492,0.059424,0,lca};
+Point(142) = {0.360504,0.059087,0,lca};
+Point(143) = {0.375655,0.058666,0,lca};
+Point(144) = {0.390928,0.058163,0,lca};
+Point(145) = {0.406309,0.057581,0,lca};
+Point(146) = {0.421783,0.056924,0,lca};
+Point(147) = {0.437333,0.056195,0,lca};
+Point(148) = {0.452946,0.055397,0,lca};
+Point(149) = {0.468605,0.054534,0,lca};
+Point(150) = {0.484295,0.053608,0,lca};
+Point(151) = {0.500000,0.052625,0,lca};
+Point(152) = {0.515705,0.051587,0,lca};
+Point(153) = {0.531395,0.050499,0,lca};
+Point(154) = {0.547054,0.049362,0,lca};
+Point(155) = {0.562667,0.048182,0,lca};
+Point(156) = {0.578217,0.046962,0,lca};
+Point(157) = {0.593691,0.045705,0,lca};
+Point(158) = {0.609072,0.044414,0,lca};
+Point(159) = {0.624345,0.043094,0,lca};
+Point(160) = {0.639496,0.041747,0,lca};
+Point(161) = {0.654508,0.040378,0,lca};
+Point(162) = {0.669369,0.038988,0,lca};
+Point(163) = {0.684062,0.037582,0,lca};
+Point(164) = {0.698574,0.036163,0,lca};
+Point(165) = {0.712890,0.034733,0,lca};
+Point(166) = {0.726995,0.033296,0,lca};
+Point(167) = {0.740877,0.031856,0,lca};
+Point(168) = {0.754521,0.030414,0,lca};
+Point(169) = {0.767913,0.028974,0,lca};
+Point(170) = {0.781042,0.027539,0,lca};
+Point(171) = {0.793893,0.026111,0,lca};
+Point(172) = {0.806454,0.024694,0,lca};
+Point(173) = {0.818712,0.023291,0,lca};
+Point(174) = {0.830656,0.021904,0,lca};
+Point(175) = {0.842274,0.020535,0,lca};
+Point(176) = {0.853553,0.019189,0,lca};
+Point(177) = {0.864484,0.017868,0,lca};
+Point(178) = {0.875056,0.016574,0,lca};
+Point(179) = {0.885257,0.015310,0,lca};
+Point(180) = {0.895078,0.014079,0,lca};
+Point(181) = {0.904508,0.012883,0,lca};
+Point(182) = {0.913540,0.011726,0,lca};
+Point(183) = {0.922164,0.010610,0,lca};
+Point(184) = {0.930371,0.009537,0,lca};
+Point(185) = {0.938153,0.008510,0,lca};
+Point(186) = {0.945503,0.007531,0,lca};
+Point(187) = {0.952414,0.006603,0,lca};
+Point(188) = {0.958877,0.005729,0,lca};
+Point(189) = {0.964888,0.004909,0,lca};
+Point(190) = {0.970440,0.004147,0,lca};
+Point(191) = {0.975528,0.003443,0,lca};
+Point(192) = {0.980147,0.002801,0,lca};
+Point(193) = {0.984292,0.002222,0,lca};
+Point(194) = {0.987958,0.001707,0,lca};
+Point(195) = {0.991144,0.001258,0,lca};
+Point(196) = {0.993844,0.000876,0,lca};
+Point(197) = {0.996057,0.000562,0,lca};
+Point(198) = {0.997781,0.000317,0,lca};
+Point(199) = {0.999013,0.000141,0,lca};
+Point(200) = {0.999753,0.000035,0,lca};
+
+//Points numerotation:
+numberLeadingEgde = 101 ;
+numberLowerSurface = 81 ;
+numberUpperSurface = 121 ;
+
+//Distances:
+distanceTrailingLowerPoint = 0.908262 ;
+distanceLowerUpperPoint = 0.222905 ;
+distanceUpperTrailingPoint = 0.908262 ;
+
+Line(1) = { 1 ... 81 };
+Line(2) = { 81 ... 101 };
+Line(3) = { 101 ... 121 };
+Line(4) = { 121 ... 200, 1 };
+
+Rotate { {0,0,1}, {1,0,0}, Incidence } { Line { 1 ... 4 } ; }
+
+/* Line Loop(1) = {1,2,3,4}; */
+/* Plane Surface(1) = {1}; */
diff --git a/Thermics/brick.geo b/Thermics/brick.geo
index 0dbaa0e..3b56f06 100644
--- a/Thermics/brick.geo
+++ b/Thermics/brick.geo
@@ -1,111 +1,111 @@
-/* -------------------------------------------------------------------
- File "brick.geo"
-
- This file is the geometrical description used by GMSH to produce
- the file "brick.msh".
- ------------------------------------------------------------------- */
-
-/* Gmsh options can be set directly in the .geo file.
- Setting "Solver.AutoMesh" to 2 ensures that GMSH systematically
- regenerates the mesh at each model execution, and does not reuse
- the mesh on disk if it exists (which is the default option).
- This option is needed in this model, because the interactive
- model parameters "Flag_Regularization" has an effect
- on the definition of the regions, which makes remeshing mandatory. */
-
-Solver.AutoMesh = 2;
-
-Include "brick_common.pro";
-
-/* The (very) simple geometry of this thermal model only contains
- rectangles. It is the opportunity to illustrate
- the function definition capabilities of Gmsh. */
-
-Function Def_Rectangle
-p1=newp; Point(newp)={xc_, yc_, 0, lc_};
-p2=newp; Point(newp)={xc_+dx_, yc_, 0, lc_};
-p3=newp; Point(newp)={xc_+dx_, yc_+dy_, 0, lc_};
-p4=newp; Point(newp)={xc_, yc_+dy_, 0, lc_};
-
-l1=newl; Line(newl)={p1,p2};
-l2=newl; Line(newl)={p2,p3};
-l3=newl; Line(newl)={p3,p4};
-l4=newl; Line(newl)={p4,p1};
-
-lines_[] = {l1, l2, l3, l4};
-
-ll1 = newll; Line Loop(ll1) = {lines_[]};
-s_ = news; Plane Surface(news) = {ll1, ll_Holes_[]};
-Return // end of Function Def_Rectangle
-
-/* Note that the code above is not parsed before it is called.
- Good practice for readability (but by no means mandatory)
- is to distinguish function variables from other variables.
- This is done here with a trailing "_" in the variable name. */
-
-
-// Window 1 (with optional layer of thickness "e_layer")
-dx_ = dx_Win1;
-dy_ = dy_Win1;
-lc_ = lc_Win1;
-xc_ = xc_Win1-dx_/2; yc_=yc_Win1-dy_/2;
-ll_Holes_[]={};
-Call Def_Rectangle;
-s_Win1 = s_;
-l_Win1[] = lines_[];
-
-If( !Flag_Regularization )
- ll_HolesForBrick[] += ll1;
-Else
- ll_HolesForLayer[] += ll1;
- dx_ = dx_Win1+2*e_layer;
- dy_ = dy_Win1+2*e_layer;
- lc_ = lc_Win1;
- xc_ = xc_Win1-dx_/2; yc_=yc_Win1-dy_/2;
-
- ll_Holes_[] = {ll_HolesForLayer[]};
- Call Def_Rectangle;
- s_Win1_Layer = s_;
- l_Win1_Layer[] = lines_[];
- ll_HolesForBrick[] += ll1;
-EndIf
-
-// Window 2
-dx_ = dx_Win2;
-dy_ = dy_Win2;
-lc_ = lc_Win2;
-xc_ = xc_Win2-dx_/2; yc_=yc_Win2-dy_/2;
-ll_Holes_[]={};
-Call Def_Rectangle;
-s_Win2 = s_;
-l_Win2[] = lines_[];
-ll_HolesForBrick[] += ll1;
-
-// Brick
-dx_ = dx_Brick; dy_ = dy_Brick;
-lc_ = lc_Brick;
-xc_ = 0; yc_ = 0;
-ll_Holes_[] = {ll_HolesForBrick[]};
-Call Def_Rectangle;
-s_Brick = s_;
-l_Brick[] = lines_[];
-
-//Printf("l_Brick", l_Brick[]);
-
-
-// Physical regions
-
-Physical Surface("Brick", 100) = {s_Brick};
-Physical Surface("Window1", 111) = {s_Win1};
-Physical Surface("Window2", 112) = {s_Win2};
-If( Flag_Regularization )
- Physical Surface("LayerWindow1", 115) = {s_Win1_Layer};
-EndIf
-
-Physical Line("Surface1", 201) = { l_Brick[{3}] };
-Physical Line("Surface2", 202) = { l_Brick[{1}] };
-Physical Line("Surface3", 203) = { l_Brick[{0}], l_Brick[{2}] };
-
-Physical Line("SurfWindow1", 211) = {l_Win1[]};
-Physical Line("SurfWindow2", 212) = {l_Win2[]};
-
+/* -------------------------------------------------------------------
+ File "brick.geo"
+
+ This file is the geometrical description used by GMSH to produce
+ the file "brick.msh".
+ ------------------------------------------------------------------- */
+
+/* Gmsh options can be set directly in the .geo file.
+ Setting "Solver.AutoMesh" to 2 ensures that GMSH systematically
+ regenerates the mesh at each model execution, and does not reuse
+ the mesh on disk if it exists (which is the default option).
+ This option is needed in this model, because the interactive
+ model parameters "Flag_Regularization" has an effect
+ on the definition of the regions, which makes remeshing mandatory. */
+
+Solver.AutoMesh = 2;
+
+Include "brick_common.pro";
+
+/* The (very) simple geometry of this thermal model only contains
+ rectangles. It is the opportunity to illustrate
+ the function definition capabilities of Gmsh. */
+
+Function Def_Rectangle
+p1=newp; Point(newp)={xc_, yc_, 0, lc_};
+p2=newp; Point(newp)={xc_+dx_, yc_, 0, lc_};
+p3=newp; Point(newp)={xc_+dx_, yc_+dy_, 0, lc_};
+p4=newp; Point(newp)={xc_, yc_+dy_, 0, lc_};
+
+l1=newl; Line(newl)={p1,p2};
+l2=newl; Line(newl)={p2,p3};
+l3=newl; Line(newl)={p3,p4};
+l4=newl; Line(newl)={p4,p1};
+
+lines_[] = {l1, l2, l3, l4};
+
+ll1 = newll; Line Loop(ll1) = {lines_[]};
+s_ = news; Plane Surface(news) = {ll1, ll_Holes_[]};
+Return // end of Function Def_Rectangle
+
+/* Note that the code above is not parsed before it is called.
+ Good practice for readability (but by no means mandatory)
+ is to distinguish function variables from other variables.
+ This is done here with a trailing "_" in the variable name. */
+
+
+// Window 1 (with optional layer of thickness "e_layer")
+dx_ = dx_Win1;
+dy_ = dy_Win1;
+lc_ = lc_Win1;
+xc_ = xc_Win1-dx_/2; yc_=yc_Win1-dy_/2;
+ll_Holes_[]={};
+Call Def_Rectangle;
+s_Win1 = s_;
+l_Win1[] = lines_[];
+
+If( !Flag_Regularization )
+ ll_HolesForBrick[] += ll1;
+Else
+ ll_HolesForLayer[] += ll1;
+ dx_ = dx_Win1+2*e_layer;
+ dy_ = dy_Win1+2*e_layer;
+ lc_ = lc_Win1;
+ xc_ = xc_Win1-dx_/2; yc_=yc_Win1-dy_/2;
+
+ ll_Holes_[] = {ll_HolesForLayer[]};
+ Call Def_Rectangle;
+ s_Win1_Layer = s_;
+ l_Win1_Layer[] = lines_[];
+ ll_HolesForBrick[] += ll1;
+EndIf
+
+// Window 2
+dx_ = dx_Win2;
+dy_ = dy_Win2;
+lc_ = lc_Win2;
+xc_ = xc_Win2-dx_/2; yc_=yc_Win2-dy_/2;
+ll_Holes_[]={};
+Call Def_Rectangle;
+s_Win2 = s_;
+l_Win2[] = lines_[];
+ll_HolesForBrick[] += ll1;
+
+// Brick
+dx_ = dx_Brick; dy_ = dy_Brick;
+lc_ = lc_Brick;
+xc_ = 0; yc_ = 0;
+ll_Holes_[] = {ll_HolesForBrick[]};
+Call Def_Rectangle;
+s_Brick = s_;
+l_Brick[] = lines_[];
+
+//Printf("l_Brick", l_Brick[]);
+
+
+// Physical regions
+
+Physical Surface("Brick", 100) = {s_Brick};
+Physical Surface("Window1", 111) = {s_Win1};
+Physical Surface("Window2", 112) = {s_Win2};
+If( Flag_Regularization )
+ Physical Surface("LayerWindow1", 115) = {s_Win1_Layer};
+EndIf
+
+Physical Line("Surface1", 201) = { l_Brick[{3}] };
+Physical Line("Surface2", 202) = { l_Brick[{1}] };
+Physical Line("Surface3", 203) = { l_Brick[{0}], l_Brick[{2}] };
+
+Physical Line("SurfWindow1", 211) = {l_Win1[]};
+Physical Line("SurfWindow2", 212) = {l_Win2[]};
+
diff --git a/Thermics/brick.pro b/Thermics/brick.pro
index 88694ac..f2720fb 100644
--- a/Thermics/brick.pro
+++ b/Thermics/brick.pro
@@ -1,454 +1,452 @@
-/* -------------------------------------------------------------------
- Tutorial 5 : thermal problem with contact resistances
-
- Features:
- - Contact resistances: scalar FunctionSpace with a surface discontinuity
- - Region with a uniform temperature (infinite thermal conductivity)
- - Computation of the heat flux through surfaces
- - Import a source field from a file
-
- To compute the solution in a terminal:
- getdp brick.pro -solve Thermal_T -pos Map_T
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > brick.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-/* This model is a rectangular brick with two windows,
- where various kinds of thermal constraints can be set.
- Dirichlet, Neumann and convection boundary conditions are imposed
- on different parts of the surface of the brick.
- The model is rather academic but it
- demonstrates some useful high-level GetDP features.
-
- Governing eqations are
-
- div ( -lambda[] grad T ) = Q in Vol_Lambda_The
- -lambda[] grad T . n = qn = 0 on Sur_Neumann_The
-
- Contact thermal resistance:
- First, it is shown how to implement contact thermal resistances
- with surface elements. The surface elements are associated with a
- thickness and a thermal conductivity (typically much lower than that
- of surrounding regions). The implementation takes advantage
- of the powerful FunctionSpace definition in GetDP.
-
- With the flag "Flag_Regularization", the contact surface
- can be, for the sake of comparison, replaced
- by a thin volume conducting region.
-
- Thermal "electrode":
- The floating potential idea (introduced in tutorial 4)
- is reconsidered here in a thermal context to represent a region
- with a very large thermal conductivity where, consequently,
- the temperature field is uniform (exactly like the electric potential
- is uniform on an electrode).
- The dual quantity of this uniform temperature "T_electrode" [K]
- (which is the "associated global quantity" in GetDP language)
- is the heat flux "Q_electrode" [W] injected in the electrode
- by the agent that maintains the temperature equal
- to the prescribed value.
-
- The value of Q_electrode is a by-product of the system resolution
- provided the term
-
- GlobalTerm { [-Dof{Q_electrode} , {T_electrode} ] ; In Tfloating_The ; }
-
- is present in the "Resolution" section. This term triggers the writing
- in the linear system of a supplementary equation associated
- with the global basis function BF{T_electrode}.
- All integrations are automatically done by getDP,
- and the value of Q_electrode is obtained in postprocessing
- with the PostOperation
-
- Print[ Q_electrode, OnRegion Tfloating_The, ... ]
-
- Heat flux through surfaces:
- The purpose of a thermal simulation usually goes beyond
- the mere calculation of a temperature distribution.
- One is in general also interested in evaluating
- the heat flux q(S) through some specific surface S:
-
- q(S) = ( -lambda[] grad T . n )_S
-
- This quantity cannot be computed from the temperature
- distribution available on the surface S only.
- As heat flux is related with the gradient of temperature
- in the direction normal to the surface, its computation relies on
- the temperature distribution in a neighborhood of the surface.
- This means that volume elements in contact with the considered surface
- need be involved in the computation.
- To achieve this with getDP, a good method proceeds
- by the definition a smooth auxiliary function g(S),
- with g(S)=1 on S, and g(S)=0 outside a finite neighborhood of S.
- Typically, g(S) is the sum of the shape functions of the nodes on S.
- Let w(S) be the support of g(S),
- and let dw(S) denote the boundary of w(S).
- We then have, just adding and substracting dw(S)
- to the surface of integration S
-
- q(S) = ( -lambda[] grad T . n g(S) )_{ dw(S) - ( dw(S)-S ) }.
-
- dw(S) being a boundary, Stokes theorem can be invoked and,
- after an integration by part one ends up with
-
- q(S) = ( -lambda[] grad T . grad g(S) )_w(S)
- - ( -lambda[] grad T . n g(S) )_{dw(S)-S}.
- + ( Q g(S) )_w(S)
-
- Now, g(S) is zero on {dw(S)-S}, except maybe at some surface elements
- adjacents to dS, but not in dS.
- The second terme vanishes then if either S is closed,
- or adjacent to a homogeneous Neumann boundary condition.
-
- The third term also vanishes, except if a region
- with a nonzero heatsource Q is in contact with the surface S.
-
- So we have nearly always the following practical formula
- to evaluate the heat flux across a surface S,
- in terms of a well-chosen auxiliary scalar function g(S).
-
- q(S) = ( -lambda[] grad T . grad g(S) )_{support of g(S)}
-
-
- Particular cases:
-
- For the heat flux through the boundary of a thermal electrode,
- one uses g(S) = BF(T_electrode).
- Note that this heat flux is equal to Q_electrode
- in the stationary case.
- This is the case for the heat flux through the boundary of Window2
-
- Auxiliary functions g(S) are also generated
- for the surfaces named "Surface_i", i=1,2,3 in the model.
- Note that the flux computed through Surface_3 is incorrect
- because this surface is not adjacent to surfaces
- with homogeneous Neumann boundary conditions.
-*/
-
-Include "brick_common.pro";
-
-QWindow1 =
- DefineNumber[1e3, Name "Window1/Heat source [W]"];
-
-/* The user is given the choice of setting either the global temperature
- or the global heat flux in Window2.
- Check how the variable "Flag_ConstraintWin2" is used at different
- places to alter the model according to that choice
- and to manage the visibility of related input and output data.*/
-QWindow2 =
- DefineNumber[1e3, Name "Window2/Heat source [W]",
- Visible Flag_ConstraintWin2];
-TWindow2 =
- DefineNumber[50, Name "Window2/Temperature [degC]",
- Visible !Flag_ConstraintWin2];
-outQWindow2 =
- DefineNumber[0, Name "Output/Q window 2 [degC]",
- Visible !Flag_ConstraintWin2, Highlight "Ivory"];
-outTWindow2 =
- DefineNumber[0, Name "Output/T window 2 [degC]",
- Visible Flag_ConstraintWin2, Highlight "Ivory"];
-
-
-ConvectionCoef =
- DefineNumber[1000, Name"Surface2/hconv",
- Label "Convection coefficient [W/(m^2K)]"];
-T_Ambiance =
- DefineNumber[20, Name"Surface2/Ambiance temperature [degC]"];
-T_Dirichlet =
- DefineNumber[20, Name"Surface1/Imposed temperature [degC]"];
-
-Group {
- /* Geometrical regions: */
- Brick = Region[100];
- LayerWindow1 = Region[115];
- Window1 = Region[111];
- Window2 = Region[112];
- SurfWindow1 = Region[211];
- SurfWindow2 = Region[212];
-
- Surface_1 = Region[201];
- Surface_2 = Region[202];
- Surface_3 = Region[203];
- NbSurface = 3;
-
- /* Abstract regions:
-
- Vol_Lambda_Ele : volume regions with a thermal conductivity lambda[]
- Sur_Dirichlet_The : Dirichlet bondary condition surface
- Sur_Neu_Ele : Neumann bondary condition surface
- Sur_Convection_The : convective surface q.n = h ( T-Tinf )
- Vol_Qsource_The : volume heat source regions
- Tfloating_The : thermal electrodes
- */
-
- Vol_Lambda_The = Region[ {Brick, Window1, Window2, LayerWindow1} ];
- Sur_Dirichlet_The = Region[ Surface_1 ];
- Sur_Neumann_The = Region[ Surface_3 ];
- Sur_Convection_The = Region[ Surface_2 ];
-
- Vol_Qsource_The = Region[ Window1 ];
- Tfloating_The = Region[ Window2 ];
-
- If( !Flag_Regularization )
- Vol_OneSide_The = Region[ Brick ];
- Sur_Tdisc_The = Region[ SurfWindow1 ];
- Else
- Vol_OneSide_The = Region[ {} ];
- Sur_Tdisc_The = Region[ {} ];
- EndIf
-}
-
-
-Function {
- lambda_Brick = 50.; // steel
- lambda[ Brick ] = lambda_Brick;
- lambda[ Region[ {Window1, Window2} ] ] = lambda_Brick ; // comment
-
- lambda_Layer = 1.0; // 50 time smaller than surrounding regions
- If( Flag_Regularization )
- lambda[ LayerWindow1 ] = lambda_Layer;
- EndIf
- lambda[ Sur_Tdisc_The ] = lambda_Layer;
- thickness[ Sur_Tdisc_The ] = e_layer;
-
- h[ Surface_2 ] = ConvectionCoef;
- Tinf[ Surface_2 ] = T_Ambiance;
-
- If( Flag_QFromFile )
- Qsource[ Window1 ] = ScalarField[XYZ[],0,1]{1};
- Else
- Qsource[ Window1 ] = 0*QWindow1/SurfaceArea[];
- EndIf
-}
-
-Constraint {
- { Name Dirichlet_The ;
- Case {
- { Region Sur_Dirichlet_The ; Value T_Dirichlet ; }
- }
- }
- { Name T_Discontinuity ;
- Case {
- { Region SurfWindow1 ; Value 20 ; }
- }
- }
- { Name T_electrode;
- Case {
- If( !Flag_ConstraintWin2 )
- { Region Window2 ; Value TWindow2 ; }
- EndIf
- }
- }
- { Name Q_electrode;
- Case {
- If( Flag_ConstraintWin2 )
- { Region Window2 ; Value QWindow2 ; }
- EndIf
- }
- }
- For i In {1:NbSurface}
- { Name FluxLayer~{i} ;
- Case {
- { Region Surface~{i} ; Value 1. ; }
- }
- }
- EndFor
-}
-
-Integration {
- { Name Int ;
- Case {
- {
- Type Gauss ;
- Case {
- { GeoElement Triangle ; NumberOfPoints 4 ; }
- { GeoElement Quadrangle ; NumberOfPoints 4 ; }
- { GeoElement Line ; NumberOfPoints 4 ; }
- }
- }
- }
- }
-}
-
-Jacobian {
- { Name Vol ;
- Case {
- { Region All ; Jacobian Vol ; }
- }
- }
- { Name Sur ;
- Case {
- { Region All ; Jacobian Sur ; }
- }
- }
-}
-
-Group {
- Dom_Hgrad_T = Region[ {Vol_Lambda_The,
- Sur_Convection_The,
- Sur_Tdisc_The} ];
- DomainWithSurf_TL_The =
- ElementsOf[ {Vol_OneSide_The, Sur_Tdisc_The},
- OnOneSideOf Sur_Tdisc_The ];
-}
-
-FunctionSpace {
- { Name Hgrad_T; Type Form0 ;
- BasisFunction {
- { Name sn ; NameOfCoef Tn ; Function BF_Node ;
- Support Dom_Hgrad_T ;
- Entity NodesOf[All, Not Tfloating_The] ; }
- { Name sf ; NameOfCoef Tf ; Function BF_GroupOfNodes ;
- Support Dom_Hgrad_T ; Entity GroupsOfNodesOf[ Tfloating_The ] ; }
- { Name sdn ; NameOfCoef Tdn ; Function BF_Node ;
- Support DomainWithSurf_TL_The ; Entity NodesOf[ Sur_Tdisc_The ] ; }
- }
- SubSpace {
- { Name Tcont ; NameOfBasisFunction { sn, sf } ; }
- { Name Tdisc ; NameOfBasisFunction { sdn } ; }
- }
- GlobalQuantity {
- { Name T_electrode ; Type AliasOf ; NameOfCoef Tf ; }
- { Name Q_electrode ; Type AssociatedWith ; NameOfCoef Tf ; }
- }
- Constraint {
- { NameOfCoef Tn ; EntityType NodesOf ;
- NameOfConstraint Dirichlet_The ; }
- // { NameOfCoef Tdn ; EntityType NodesOf ; //
- // NameOfConstraint T_Discontinuity ; } //
- { NameOfCoef T_electrode ; EntityType GroupsOfNodesOf ;
- NameOfConstraint T_electrode ; }
- { NameOfCoef Q_electrode ; EntityType GroupsOfNodesOf ;
- NameOfConstraint Q_electrode ; }
- }
- }
- For i In {1:NbSurface}
- { Name FluxLayer~{i} ; Type Form0 ;
- BasisFunction {
- { Name gn ; NameOfCoef un ; Function BF_GroupOfNodes;
- Support Dom_Hgrad_T ; Entity GroupsOfNodesOf[ Surface~{i} ] ; }
- }
- Constraint {
- { NameOfCoef un ; EntityType GroupsOfNodesOf ;
- NameOfConstraint FluxLayer~{i} ; }
- }
- }
- EndFor
-
-}
-
-Formulation {
- { Name Thermal_T ; Type FemEquation ;
- Quantity {
- { Name T ; Type Local ; NameOfSpace Hgrad_T ; }
- { Name Tcont ; Type Local ; NameOfSpace Hgrad_T[Tcont] ; }
- { Name Tdisc ; Type Local ; NameOfSpace Hgrad_T[Tdisc] ; }
- { Name Tglob ; Type Global ; NameOfSpace Hgrad_T[T_electrode] ; }
- { Name Qglob ; Type Global ; NameOfSpace Hgrad_T[Q_electrode] ; }
- For i In {1:NbSurface}
- { Name un~{i} ; Type Local ; NameOfSpace FluxLayer~{i} ; }
- EndFor
-
- }
- Equation {
-
- Galerkin { [ lambda[] * Dof{d T} , {d T} ] ;
- In Vol_Lambda_The; Integration Int ; Jacobian Vol ; }
-
- Galerkin { [ ( lambda[]/thickness[] ) * Dof{Tdisc} , {Tdisc} ] ;
- In Sur_Tdisc_The; Integration Int ; Jacobian Sur ; }
-
- Galerkin { [ -Qsource[] , {T} ] ;
- In Vol_Qsource_The ; Integration Int ; Jacobian Vol ; }
-
- Galerkin { [ h[] * Dof{T} , {T} ] ;
- In Sur_Convection_The ; Integration Int ; Jacobian Sur ; }
-
- Galerkin { [ -h[] * Tinf[] , {T} ] ;
- In Sur_Convection_The ; Integration Int ; Jacobian Sur ; }
-
- GlobalTerm { [-Dof{Qglob} , {Tglob} ] ; In Tfloating_The ; }
-
- For i In {1:NbSurface}
- Galerkin { [ 0 * Dof{un~{i}} , {un~{i}} ] ;
- In Vol_Lambda_The ; Integration Int ; Jacobian Vol ; }
- EndFor
- }
- }
-}
-
-
-Resolution {
- { Name Thermal_T ;
- System {
- { Name Sys_The ; NameOfFormulation Thermal_T ; }
- }
- Operation {
- If( Flag_QFromFile )
- GmshRead[ "Q.pos", 1];
- EndIf
- DeleteFile["output.txt"];
- Generate Sys_The ; Solve Sys_The ; SaveSolution Sys_The ;
- }
- }
-}
-
-PostProcessing {
- { Name Thermal_T ; NameOfFormulation Thermal_T ;
- PostQuantity {
- { Name T ; Value { Term { [ {T} ] ;
- In Dom_Hgrad_T ; Jacobian Vol ; } } }
- { Name q ; Value { Term { [ -lambda[] * {d T} ] ;
- In Dom_Hgrad_T ; Jacobian Vol ; } } }
- { Name Tcont ; Value { Term { [ {Tcont} ] ;
- In Dom_Hgrad_T ; Jacobian Vol ; } } }
- { Name Tdisc ; Value { Term { [ {Tdisc} ] ;
- In Dom_Hgrad_T ; Jacobian Vol ; } } }
- { Name Qglob; Value { Term { [ {Qglob} ]; In Tfloating_The; } } }
- { Name Tglob; Value { Term { [ {Tglob} ]; In Tfloating_The; } } }
-
- For i In {1:NbSurface}
- { Name un~{i} ; Value { Local { [ {un~{i}} ] ;
- In Vol_Lambda_The ; Jacobian Vol ; } } }
- { Name IFlux~{i} ; Value { Integral { [ -lambda[]*{d T} * {d un~{i}} ];
- In Vol_Lambda_The ; Jacobian Vol ; Integration Int ; } } }
- EndFor
-
- }
- }
-}
-
-PostOperation Map_T UsingPost Thermal_T {
- If( !Flag_Regularization )
- Print[ Tcont, OnElementsOf Vol_Lambda_The, File "Tcont.pos"] ;
- Print[ Tdisc, OnElementsOf Vol_Lambda_The, File "Tdisc.pos"] ;
- EndIf
-
- If(Flag_ConstraintWin2)
- Print[ Tglob, OnRegion Tfloating_The, File > "output.txt", Color "Ivory",
- Format Table, SendToServer "Output/T window 2 [degC]" ];
- Else
- Print[ Qglob, OnRegion Tfloating_The, File > "output.txt", Color "Ivory",
- Format Table, SendToServer "Output/Q window 2 [degC]" ];
- EndIf
-
- For i In {1:NbSurface}
- Print[un~{i}, OnElementsOf Vol_Lambda_The,
- File Sprintf("FluxLayer_%g.pos",i)];
- Print[ IFlux~{i}[Vol_Lambda_The], OnGlobal,
- Format TimeTable, File > "Fluxes.dat", Color "Ivory",
- SendToServer Sprintf("Output/Heat flux surface %g [W]", i)];
- EndFor
- Print[ T, OnElementsOf Vol_Lambda_The, File "T.pos" ] ;
- Echo[ StrCat["l=PostProcessing.NbViews-1;",
- "View[l].IntervalsType = 3;",
- "View[l].NbIso = 30;",
- "View[l].NormalRaise = 0.0005;"],
- File "tmp.geo", LastTimeStepOnly] ;
- Print [ q, OnLine {{0.02,0.0001,0}{0.02,0.05,0}} {200},
- Format SimpleTable, File "Cut.txt" ];
-}
-
-
+/* -------------------------------------------------------------------
+ Tutorial 5 : thermal problem with contact resistances
+
+ Features:
+ - Contact resistances: scalar FunctionSpace with a surface discontinuity
+ - Region with a uniform temperature (infinite thermal conductivity)
+ - Computation of the heat flux through surfaces
+ - Import a source field from a file
+
+ To compute the solution in a terminal:
+ getdp brick.pro -solve Thermal_T -pos Map_T
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > brick.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+/* This model is a rectangular brick with two windows,
+ where various kinds of thermal constraints can be set.
+ Dirichlet, Neumann and convection boundary conditions are imposed
+ on different parts of the surface of the brick.
+ The model is rather academic but it
+ demonstrates some useful high-level GetDP features.
+
+ Governing eqations are
+
+ div ( -lambda[] grad T ) = Q in Vol_Lambda_The
+ -lambda[] grad T . n = qn = 0 on Sur_Neumann_The
+
+ Contact thermal resistance:
+ First, it is shown how to implement contact thermal resistances
+ with surface elements. The surface elements are associated with a
+ thickness and a thermal conductivity (typically much lower than that
+ of surrounding regions). The implementation takes advantage
+ of the powerful FunctionSpace definition in GetDP.
+
+ With the flag "Flag_Regularization", the contact surface
+ can be, for the sake of comparison, replaced
+ by a thin volume conducting region.
+
+ Thermal "electrode":
+ The floating potential idea (introduced in tutorial 4)
+ is reconsidered here in a thermal context to represent a region
+ with a very large thermal conductivity where, consequently,
+ the temperature field is uniform (exactly like the electric potential
+ is uniform on an electrode).
+ The dual quantity of this uniform temperature "T_electrode" [K]
+ (which is the "associated global quantity" in GetDP language)
+ is the heat flux "Q_electrode" [W] injected in the electrode
+ by the agent that maintains the temperature equal
+ to the prescribed value.
+
+ The value of Q_electrode is a by-product of the system resolution
+ provided the term
+
+ GlobalTerm { [-Dof{Q_electrode} , {T_electrode} ] ; In Tfloating_The ; }
+
+ is present in the "Resolution" section. This term triggers the writing
+ in the linear system of a supplementary equation associated
+ with the global basis function BF{T_electrode}.
+ All integrations are automatically done by getDP,
+ and the value of Q_electrode is obtained in postprocessing
+ with the PostOperation
+
+ Print[ Q_electrode, OnRegion Tfloating_The, ... ]
+
+ Heat flux through surfaces:
+ The purpose of a thermal simulation usually goes beyond
+ the mere calculation of a temperature distribution.
+ One is in general also interested in evaluating
+ the heat flux q(S) through some specific surface S:
+
+ q(S) = ( -lambda[] grad T . n )_S
+
+ This quantity cannot be computed from the temperature
+ distribution available on the surface S only.
+ As heat flux is related with the gradient of temperature
+ in the direction normal to the surface, its computation relies on
+ the temperature distribution in a neighborhood of the surface.
+ This means that volume elements in contact with the considered surface
+ need be involved in the computation.
+ To achieve this with getDP, a good method proceeds
+ by the definition a smooth auxiliary function g(S),
+ with g(S)=1 on S, and g(S)=0 outside a finite neighborhood of S.
+ Typically, g(S) is the sum of the shape functions of the nodes on S.
+ Let w(S) be the support of g(S),
+ and let dw(S) denote the boundary of w(S).
+ We then have, just adding and substracting dw(S)
+ to the surface of integration S
+
+ q(S) = ( -lambda[] grad T . n g(S) )_{ dw(S) - ( dw(S)-S ) }.
+
+ dw(S) being a boundary, Stokes theorem can be invoked and,
+ after an integration by part one ends up with
+
+ q(S) = ( -lambda[] grad T . grad g(S) )_w(S)
+ - ( -lambda[] grad T . n g(S) )_{dw(S)-S}.
+ + ( Q g(S) )_w(S)
+
+ Now, g(S) is zero on {dw(S)-S}, except maybe at some surface elements
+ adjacents to dS, but not in dS.
+ The second terme vanishes then if either S is closed,
+ or adjacent to a homogeneous Neumann boundary condition.
+
+ The third term also vanishes, except if a region
+ with a nonzero heatsource Q is in contact with the surface S.
+
+ So we have nearly always the following practical formula
+ to evaluate the heat flux across a surface S,
+ in terms of a well-chosen auxiliary scalar function g(S).
+
+ q(S) = ( -lambda[] grad T . grad g(S) )_{support of g(S)}
+
+
+ Particular cases:
+
+ For the heat flux through the boundary of a thermal electrode,
+ one uses g(S) = BF(T_electrode).
+ Note that this heat flux is equal to Q_electrode
+ in the stationary case.
+ This is the case for the heat flux through the boundary of Window2
+
+ Auxiliary functions g(S) are also generated
+ for the surfaces named "Surface_i", i=1,2,3 in the model.
+ Note that the flux computed through Surface_3 is incorrect
+ because this surface is not adjacent to surfaces
+ with homogeneous Neumann boundary conditions.
+*/
+
+Include "brick_common.pro";
+
+QWindow1 =
+ DefineNumber[1e3, Name "Window1/Heat source [W]"];
+
+/* The user is given the choice of setting either the global temperature
+ or the global heat flux in Window2.
+ Check how the variable "Flag_ConstraintWin2" is used at different
+ places to alter the model according to that choice
+ and to manage the visibility of related input and output data.*/
+QWindow2 =
+ DefineNumber[1e3, Name "Window2/Heat source [W]",
+ Visible Flag_ConstraintWin2];
+TWindow2 =
+ DefineNumber[50, Name "Window2/Temperature [degC]",
+ Visible !Flag_ConstraintWin2];
+outQWindow2 =
+ DefineNumber[0, Name "Output/Q window 2 [degC]",
+ Visible !Flag_ConstraintWin2, Highlight "Ivory"];
+outTWindow2 =
+ DefineNumber[0, Name "Output/T window 2 [degC]",
+ Visible Flag_ConstraintWin2, Highlight "Ivory"];
+
+
+ConvectionCoef =
+ DefineNumber[1000, Name"Surface2/hconv",
+ Label "Convection coefficient [W/(m^2K)]"];
+T_Ambiance =
+ DefineNumber[20, Name"Surface2/Ambiance temperature [degC]"];
+T_Dirichlet =
+ DefineNumber[20, Name"Surface1/Imposed temperature [degC]"];
+
+Group {
+ /* Geometrical regions: */
+ Brick = Region[100];
+ LayerWindow1 = Region[115];
+ Window1 = Region[111];
+ Window2 = Region[112];
+ SurfWindow1 = Region[211];
+ SurfWindow2 = Region[212];
+
+ Surface_1 = Region[201];
+ Surface_2 = Region[202];
+ Surface_3 = Region[203];
+ NbSurface = 3;
+
+ /* Abstract regions:
+
+ Vol_Lambda_Ele : volume regions with a thermal conductivity lambda[]
+ Sur_Dirichlet_The : Dirichlet bondary condition surface
+ Sur_Neu_Ele : Neumann bondary condition surface
+ Sur_Convection_The : convective surface q.n = h ( T-Tinf )
+ Vol_Qsource_The : volume heat source regions
+ Tfloating_The : thermal electrodes
+ */
+
+ Vol_Lambda_The = Region[ {Brick, Window1, Window2, LayerWindow1} ];
+ Sur_Dirichlet_The = Region[ Surface_1 ];
+ Sur_Neumann_The = Region[ Surface_3 ];
+ Sur_Convection_The = Region[ Surface_2 ];
+
+ Vol_Qsource_The = Region[ Window1 ];
+ Tfloating_The = Region[ Window2 ];
+
+ If( !Flag_Regularization )
+ Vol_OneSide_The = Region[ Brick ];
+ Sur_Tdisc_The = Region[ SurfWindow1 ];
+ Else
+ Vol_OneSide_The = Region[ {} ];
+ Sur_Tdisc_The = Region[ {} ];
+ EndIf
+}
+
+
+Function {
+ lambda_Brick = 50.; // steel
+ lambda[ Brick ] = lambda_Brick;
+ lambda[ Region[ {Window1, Window2} ] ] = lambda_Brick ; // comment
+
+ lambda_Layer = 1.0; // 50 time smaller than surrounding regions
+ If( Flag_Regularization )
+ lambda[ LayerWindow1 ] = lambda_Layer;
+ EndIf
+ lambda[ Sur_Tdisc_The ] = lambda_Layer;
+ thickness[ Sur_Tdisc_The ] = e_layer;
+
+ h[ Surface_2 ] = ConvectionCoef;
+ Tinf[ Surface_2 ] = T_Ambiance;
+
+ If( Flag_QFromFile )
+ Qsource[ Window1 ] = ScalarField[XYZ[],0,1]{1};
+ Else
+ Qsource[ Window1 ] = 0*QWindow1/SurfaceArea[];
+ EndIf
+}
+
+Constraint {
+ { Name Dirichlet_The ;
+ Case {
+ { Region Sur_Dirichlet_The ; Value T_Dirichlet ; }
+ }
+ }
+ { Name T_Discontinuity ;
+ Case {
+ { Region SurfWindow1 ; Value 20 ; }
+ }
+ }
+ { Name T_electrode;
+ Case {
+ If( !Flag_ConstraintWin2 )
+ { Region Window2 ; Value TWindow2 ; }
+ EndIf
+ }
+ }
+ { Name Q_electrode;
+ Case {
+ If( Flag_ConstraintWin2 )
+ { Region Window2 ; Value QWindow2 ; }
+ EndIf
+ }
+ }
+ For i In {1:NbSurface}
+ { Name FluxLayer~{i} ;
+ Case {
+ { Region Surface~{i} ; Value 1. ; }
+ }
+ }
+ EndFor
+}
+
+Integration {
+ { Name Int ;
+ Case {
+ {
+ Type Gauss ;
+ Case {
+ { GeoElement Triangle ; NumberOfPoints 4 ; }
+ { GeoElement Quadrangle ; NumberOfPoints 4 ; }
+ { GeoElement Line ; NumberOfPoints 4 ; }
+ }
+ }
+ }
+ }
+}
+
+Jacobian {
+ { Name Vol ;
+ Case {
+ { Region All ; Jacobian Vol ; }
+ }
+ }
+ { Name Sur ;
+ Case {
+ { Region All ; Jacobian Sur ; }
+ }
+ }
+}
+
+Group {
+ Dom_Hgrad_T = Region[ {Vol_Lambda_The,
+ Sur_Convection_The,
+ Sur_Tdisc_The} ];
+ DomainWithSurf_TL_The =
+ ElementsOf[ {Vol_OneSide_The, Sur_Tdisc_The},
+ OnOneSideOf Sur_Tdisc_The ];
+}
+
+FunctionSpace {
+ { Name Hgrad_T; Type Form0 ;
+ BasisFunction {
+ { Name sn ; NameOfCoef Tn ; Function BF_Node ;
+ Support Dom_Hgrad_T ;
+ Entity NodesOf[All, Not Tfloating_The] ; }
+ { Name sf ; NameOfCoef Tf ; Function BF_GroupOfNodes ;
+ Support Dom_Hgrad_T ; Entity GroupsOfNodesOf[ Tfloating_The ] ; }
+ { Name sdn ; NameOfCoef Tdn ; Function BF_Node ;
+ Support DomainWithSurf_TL_The ; Entity NodesOf[ Sur_Tdisc_The ] ; }
+ }
+ SubSpace {
+ { Name Tcont ; NameOfBasisFunction { sn, sf } ; }
+ { Name Tdisc ; NameOfBasisFunction { sdn } ; }
+ }
+ GlobalQuantity {
+ { Name T_electrode ; Type AliasOf ; NameOfCoef Tf ; }
+ { Name Q_electrode ; Type AssociatedWith ; NameOfCoef Tf ; }
+ }
+ Constraint {
+ { NameOfCoef Tn ; EntityType NodesOf ;
+ NameOfConstraint Dirichlet_The ; }
+ // { NameOfCoef Tdn ; EntityType NodesOf ; //
+ // NameOfConstraint T_Discontinuity ; } //
+ { NameOfCoef T_electrode ; EntityType GroupsOfNodesOf ;
+ NameOfConstraint T_electrode ; }
+ { NameOfCoef Q_electrode ; EntityType GroupsOfNodesOf ;
+ NameOfConstraint Q_electrode ; }
+ }
+ }
+ For i In {1:NbSurface}
+ { Name FluxLayer~{i} ; Type Form0 ;
+ BasisFunction {
+ { Name gn ; NameOfCoef un ; Function BF_GroupOfNodes;
+ Support Dom_Hgrad_T ; Entity GroupsOfNodesOf[ Surface~{i} ] ; }
+ }
+ Constraint {
+ { NameOfCoef un ; EntityType GroupsOfNodesOf ;
+ NameOfConstraint FluxLayer~{i} ; }
+ }
+ }
+ EndFor
+
+}
+
+Formulation {
+ { Name Thermal_T ; Type FemEquation ;
+ Quantity {
+ { Name T ; Type Local ; NameOfSpace Hgrad_T ; }
+ { Name Tcont ; Type Local ; NameOfSpace Hgrad_T[Tcont] ; }
+ { Name Tdisc ; Type Local ; NameOfSpace Hgrad_T[Tdisc] ; }
+ { Name Tglob ; Type Global ; NameOfSpace Hgrad_T[T_electrode] ; }
+ { Name Qglob ; Type Global ; NameOfSpace Hgrad_T[Q_electrode] ; }
+ For i In {1:NbSurface}
+ { Name un~{i} ; Type Local ; NameOfSpace FluxLayer~{i} ; }
+ EndFor
+
+ }
+ Equation {
+
+ Integral { [ lambda[] * Dof{d T} , {d T} ] ;
+ In Vol_Lambda_The; Integration Int ; Jacobian Vol ; }
+
+ Integral { [ ( lambda[]/thickness[] ) * Dof{Tdisc} , {Tdisc} ] ;
+ In Sur_Tdisc_The; Integration Int ; Jacobian Sur ; }
+
+ Integral { [ -Qsource[] , {T} ] ;
+ In Vol_Qsource_The ; Integration Int ; Jacobian Vol ; }
+
+ Integral { [ h[] * Dof{T} , {T} ] ;
+ In Sur_Convection_The ; Integration Int ; Jacobian Sur ; }
+
+ Integral { [ -h[] * Tinf[] , {T} ] ;
+ In Sur_Convection_The ; Integration Int ; Jacobian Sur ; }
+
+ GlobalTerm { [-Dof{Qglob} , {Tglob} ] ; In Tfloating_The ; }
+
+ For i In {1:NbSurface}
+ Integral { [ 0 * Dof{un~{i}} , {un~{i}} ] ;
+ In Vol_Lambda_The ; Integration Int ; Jacobian Vol ; }
+ EndFor
+ }
+ }
+}
+
+
+Resolution {
+ { Name Thermal_T ;
+ System {
+ { Name Sys_The ; NameOfFormulation Thermal_T ; }
+ }
+ Operation {
+ If( Flag_QFromFile )
+ GmshRead[ "Q.pos", 1];
+ EndIf
+ DeleteFile["output.txt"];
+ Generate Sys_The ; Solve Sys_The ; SaveSolution Sys_The ;
+ }
+ }
+}
+
+PostProcessing {
+ { Name Thermal_T ; NameOfFormulation Thermal_T ;
+ PostQuantity {
+ { Name T ; Value { Term { [ {T} ] ;
+ In Dom_Hgrad_T ; Jacobian Vol ; } } }
+ { Name q ; Value { Term { [ -lambda[] * {d T} ] ;
+ In Dom_Hgrad_T ; Jacobian Vol ; } } }
+ { Name Tcont ; Value { Term { [ {Tcont} ] ;
+ In Dom_Hgrad_T ; Jacobian Vol ; } } }
+ { Name Tdisc ; Value { Term { [ {Tdisc} ] ;
+ In Dom_Hgrad_T ; Jacobian Vol ; } } }
+ { Name Qglob; Value { Term { [ {Qglob} ]; In Tfloating_The; } } }
+ { Name Tglob; Value { Term { [ {Tglob} ]; In Tfloating_The; } } }
+
+ For i In {1:NbSurface}
+ { Name un~{i} ; Value { Local { [ {un~{i}} ] ;
+ In Vol_Lambda_The ; Jacobian Vol ; } } }
+ { Name IFlux~{i} ; Value { Integral { [ -lambda[]*{d T} * {d un~{i}} ];
+ In Vol_Lambda_The ; Jacobian Vol ; Integration Int ; } } }
+ EndFor
+
+ }
+ }
+}
+
+PostOperation Map_T UsingPost Thermal_T {
+ If( !Flag_Regularization )
+ Print[ Tcont, OnElementsOf Vol_Lambda_The, File "Tcont.pos"] ;
+ Print[ Tdisc, OnElementsOf Vol_Lambda_The, File "Tdisc.pos"] ;
+ EndIf
+
+ If(Flag_ConstraintWin2)
+ Print[ Tglob, OnRegion Tfloating_The, File > "output.txt", Color "Ivory",
+ Format Table, SendToServer "Output/T window 2 [degC]" ];
+ Else
+ Print[ Qglob, OnRegion Tfloating_The, File > "output.txt", Color "Ivory",
+ Format Table, SendToServer "Output/Q window 2 [degC]" ];
+ EndIf
+
+ For i In {1:NbSurface}
+ Print[un~{i}, OnElementsOf Vol_Lambda_The,
+ File Sprintf("FluxLayer_%g.pos",i)];
+ Print[ IFlux~{i}[Vol_Lambda_The], OnGlobal,
+ Format TimeTable, File > "Fluxes.dat", Color "Ivory",
+ SendToServer Sprintf("Output/Heat flux surface %g [W]", i)];
+ EndFor
+ Print[ T, OnElementsOf Vol_Lambda_The, File "T.pos" ] ;
+ Echo[ StrCat["l=PostProcessing.NbViews-1;",
+ "View[l].IntervalsType = 3;",
+ "View[l].NbIso = 30;",
+ "View[l].NormalRaise = 0.0005;"],
+ File "tmp.geo", LastTimeStepOnly] ;
+ Print [ q, OnLine {{0.02,0.0001,0}{0.02,0.05,0}} {200},
+ Format SimpleTable, File "Cut.txt" ];
+}
diff --git a/Thermics/brick_common.pro b/Thermics/brick_common.pro
index 09a999c..4efa98e 100644
--- a/Thermics/brick_common.pro
+++ b/Thermics/brick_common.pro
@@ -1,37 +1,37 @@
-
-// Onelab parameters
-
-Flag_Regularization =
- DefineNumber[0, Name "Options/Regularize field", Choices {0,1} ];
-Flag_QFromFile =
- DefineNumber[0, Name "Options/Heat source from file", Choices {0,1} ];
-Flag_ConstraintWin2 =
- DefineNumber[0, Name "Options/Constraint in Window2",
- Choices {0="Fixed temperature", 1="Fixed heat flux"} ];
-MeshRefinement =
- DefineNumber[1, Name "Options/0Mesh refinement",
- Help "Choose 1 for a coarse mesh and 0.1 for a fine mesh."];
-
-// Geometrical dimensions
-
-mm=1e-3; // mm to m conversion factor
-
-dx_Brick=100*mm; dy_Brick= 50*mm;
-e_layer = 1*mm;
-dx_Win1 = 20*mm; dy_Win1 = 20*mm;
-If( Flag_Regularization )
- dx_Win1 += e_layer;
- dy_Win1 += e_layer;
-EndIf
-
-dx_Win2 = 20*mm; dy_Win2 = 20*mm;
-xc_Win1 = 25*mm; yc_Win1 = dy_Brick/2;
-xc_Win2 = 75*mm; yc_Win2 = dy_Brick/2;
-
-// Element sizes
-
-s=1;
-lc_Brick = dy_Brick/20 *s;
-lc_Win1 = dx_Win1/10 *s;
-lc_Win2 = dx_Win2/10 *s;
-
+
+// Onelab parameters
+
+Flag_Regularization =
+ DefineNumber[0, Name "Options/Regularize field", Choices {0,1} ];
+Flag_QFromFile =
+ DefineNumber[0, Name "Options/Heat source from file", Choices {0,1} ];
+Flag_ConstraintWin2 =
+ DefineNumber[0, Name "Options/Constraint in Window2",
+ Choices {0="Fixed temperature", 1="Fixed heat flux"} ];
+MeshRefinement =
+ DefineNumber[1, Name "Options/0Mesh refinement",
+ Help "Choose 1 for a coarse mesh and 0.1 for a fine mesh."];
+
+// Geometrical dimensions
+
+mm=1e-3; // mm to m conversion factor
+
+dx_Brick=100*mm; dy_Brick= 50*mm;
+e_layer = 1*mm;
+dx_Win1 = 20*mm; dy_Win1 = 20*mm;
+If( Flag_Regularization )
+ dx_Win1 += e_layer;
+ dy_Win1 += e_layer;
+EndIf
+
+dx_Win2 = 20*mm; dy_Win2 = 20*mm;
+xc_Win1 = 25*mm; yc_Win1 = dy_Brick/2;
+xc_Win2 = 75*mm; yc_Win2 = dy_Brick/2;
+
+// Element sizes
+
+s=1;
+lc_Brick = dy_Brick/20 *s;
+lc_Win1 = dx_Win1/10 *s;
+lc_Win2 = dx_Win2/10 *s;
+
--
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