diff --git a/MagneticForces/magnets.pro b/MagneticForces/magnets.pro
index b1703c2169ccf47356b33d7f270fac8ed44f9316..1ce7561d76042df719094002bdfddc03c088fd55 100644
--- a/MagneticForces/magnets.pro
+++ b/MagneticForces/magnets.pro
@@ -2,13 +2,13 @@
Tutorial 9 : 3D magnetostatic dual formulations and magnetic forces
Features:
- - 3D Magnetostatics
+ - 3D Magnetostatics
- Dual vector and scalar magnetic potentials formulations
- Boundary condition at infinity with infinite elements
- Maxwell stress tensor and rigid-body magnetic forces
To compute the solution in a terminal:
- First generate the (3D) mesh and then run getdp with the chosen resolution
+ First generate the (3D) mesh and then run getdp with the chosen resolution
gmsh magnets.geo -3
getdp magnets.pro -solve MagSta_a
OR
@@ -16,67 +16,66 @@
To compute the solution interactively from the Gmsh GUI:
File > Open > magnets.pro
- Resolution can be chosen from the menu on the left:
+ Resolution can be chosen from the menu on the left:
MagSta_a (default) or MagSta_phi
Run (button at the bottom of the left panel)
------------------------------------------------------------------- */
/*
- This tutorial solves the electromagnetic field
- and the rigid-body forces acting on a set of magnetic pieces
- of either parallelepipedic or cylindrical shape.
- Besides position and dimension, each piece is attributed
- a (constant) magnetic permeability and/or a remanence field.
- Hereafter, the pieces are all, simply though imprecisely, referred to as "Magnet",
- irresective of whether they are truly permanent magnets or ferromagnetic barrels.
+ This tutorial solves the electromagnetic field and the rigid-body forces acting
+ on a set of magnetic pieces of either parallelepipedic or cylindrical shape.
+ Besides position and dimension, each piece is attributed a (constant) magnetic
+ permeability and/or a remanence field. Hereafter, the pieces are all, simply
+ though imprecisely, referred to as "Magnet", irresective of whether they are
+ truly permanent magnets or ferromagnetic barrels.
The tutorial model proposes two dual 3D magnetostatic formulations:
+
- the magnetic vector potential formulation with spanning-tree gauging;
- the scalar magnetic potential formulation.
- As there are no conductors, the later is rather simple. The source field "hs" is
- directly the the known coercive field hc[]:
-
+
+ As there are no conductors, the later is rather simple. The source field "hs"
+ is directly the the known coercive field hc[]:
+
h = hs - grad phi , hs = -hc.
- If the "Add infinite box" box is ticked, a transformation to infinity shell is
- used to impose the exact zero-field boundary condition at infinity.
- See also Tutorial 2: magnetostatic field of an electromagnet.
- The shell is generated automatically by including "InfiniteBox.geo"
- at the end of the geometrical description of the model.
- It can be placed rather close of the magnets without loss of accuracy.
-
- The preferred way to compute electromagnetic forces in GetDP
- is as an explicit by-product of the Maxwell stress tensor "TM[{b}]",
- which is a material dependent function of the magnetic induction "b" field.
- The magnetic force acting on a rigid body in empty space can be evaluated
- as the flux of the Maxwell stress tensor through a surface "S" (surrounding the body).
- A special auxiliary function "g(S)" linked "S" is defined for each magnet, i.e.
- "g(SkinMagnet~{i}) = un~{i}".
- The resultant magnetic force acting on "Magnet~{i}" is given by the integral:
+ If the "Add infinite box" box is ticked, a transformation to infinity shell is
+ used to impose the exact zero-field boundary condition at infinity. See also
+ Tutorial 2: magnetostatic field of an electromagnet. The shell is generated
+ automatically by including "InfiniteBox.geo" at the end of the geometrical
+ description of the model. It can be placed rather close of the magnets without
+ loss of accuracy.
+
+ The preferred way to compute electromagnetic forces in GetDP is as an explicit
+ by-product of the Maxwell stress tensor "TM[{b}]", which is a material
+ dependent function of the magnetic induction "b" field. The magnetic force
+ acting on a rigid body in empty space can be evaluated as the flux of the
+ Maxwell stress tensor through a surface "S" (surrounding the body). A special
+ auxiliary function "g(S)" linked "S" is defined for each magnet, i.e.
+ "g(SkinMagnet~{i}) = un~{i}". The resultant magnetic force acting on
+ "Magnet~{i}" is given by the integral:
f~{i} = Integral [ TM[{b}] * {-grad un~{i}} ] ;
-
- This approach is analogous to the computation of heat flux "q(S)" through a
- surface "S" described in "Tutorial 5: thermal problem with contact resistances".
-
- Note that the Maxwell stress tensor is always discontinuous on material discontinuities,
- and that magnetic forces acting on rigid bodies
- depend only on the Maxwell stress tensor in empty space,
- and on the "b" and "h" field distribution,
- on the external side of "SkinMagnet~{i}"
- (side of the surface in contact with air).
-
- "{-grad un~{i}}" in the above formula can be regarded
- as the normal vector to "SkinMagnet~{i}"
- in the one element thick layer "layer~{i}" of finite elements
- around "Magnet~{i}", and "f~{i}", is thus indeed the flux of "TM[]"
- through the surface of "Magnet~{i}".
-
- The support of "{-grad un~{i}}" is limited to "layer~{i}",
- which is much smaller than "AirBox".
- To speed up the computation of forces, a special domain "Vol_Force"
- for force integrations is defined, which contains only
- the layers "layer~{i}" of all magnets.
+
+ This approach is analogous to the computation of heat flux "q(S)" through a
+ surface "S" described in "Tutorial 5: thermal problem with contact
+ resistances".
+
+ Note that the Maxwell stress tensor is always discontinuous on material
+ discontinuities, and that magnetic forces acting on rigid bodies depend only on
+ the Maxwell stress tensor in empty space, and on the "b" and "h" field
+ distribution, on the external side of "SkinMagnet~{i}" (side of the surface in
+ contact with air).
+
+ "{-grad un~{i}}" in the above formula can be regarded as the normal vector to
+ "SkinMagnet~{i}" in the one element thick layer "layer~{i}" of finite elements
+ around "Magnet~{i}", and "f~{i}", is thus indeed the flux of "TM[]" through the
+ surface of "Magnet~{i}".
+
+ The support of "{-grad un~{i}}" is limited to "layer~{i}", which is much
+ smaller than "AirBox". To speed up the computation of forces, a special domain
+ "Vol_Force" for force integrations is defined, which contains only the layers
+ "layer~{i}" of all magnets.
*/
Include "magnets_common.pro"
@@ -98,20 +97,20 @@ Group{
Outer = Region[5];
For i In {1:NumMagnets}
- Magnet~{i} = Region[ {(10*i)}];
+ Magnet~{i} = Region[ {(10*i)}];
SkinMagnet~{i} = Region[ {(10*i+1)} ];
Layer~{i} = Region[AirBox, OnOneSideOf SkinMagnet~{i}] ;
EndFor
// Abstract Groups (group geometrical regions into formulation relevant groups)
- Vol_Inf = Region[ {domInfX, domInfY, domInfZ} ];
+ Vol_Inf = Region[ {domInfX, domInfY, domInfZ} ];
Vol_Air = Region[ {AirBox, Vol_Inf} ];
Vol_Magnet = Region[{}];
Sur_Magnet = Region[{}];
Vol_Force = Region[{}];
For i In {1:NumMagnets}
- Sur_Magnet += Region[SkinMagnet~{i}];
+ Sur_Magnet += Region[SkinMagnet~{i}];
Vol_Magnet += Region[Magnet~{i}];
Vol_Layer += Region[Layer~{i}];
EndFor
@@ -152,7 +151,7 @@ Jacobian {
{ Name Vol ;
Case {
{ Region All ; Jacobian Vol ; }
- {Region domInfX; Jacobian VolRectShell {xInt,xExt,1,xCnt,yCnt,zCnt};}
+ {Region domInfX; Jacobian VolRectShell {xInt,xExt,1,xCnt,yCnt,zCnt};}
{Region domInfY; Jacobian VolRectShell {yInt,yExt,2,xCnt,yCnt,zCnt};}
{Region domInfZ; Jacobian VolRectShell {zInt,zExt,3,xCnt,yCnt,zCnt};}
}
@@ -160,7 +159,7 @@ Jacobian {
}
Integration {
- { Name Int ;
+ { Name Int ;
Case {
{ Type Gauss ;
Case {
@@ -168,7 +167,7 @@ Integration {
{ GeoElement Quadrangle ; NumberOfPoints 4 ; }
{ GeoElement Tetrahedron ; NumberOfPoints 4 ; }
{ GeoElement Hexahedron ; NumberOfPoints 6 ; }
- { GeoElement Prism ; NumberOfPoints 6 ; }
+ { GeoElement Prism ; NumberOfPoints 6 ; }
}
}
}
@@ -212,7 +211,7 @@ FunctionSpace {
}
{ Name Hcurl_a; Type Form1; // magnetic vector potential
BasisFunction {
- { Name se; NameOfCoef ae; Function BF_Edge;
+ { Name se; NameOfCoef ae; Function BF_Edge;
Support Dom_Hcurl_a ;Entity EdgesOf[ All ]; }
}
Constraint {
@@ -268,7 +267,7 @@ Formulation {
In Vol_mu ; Jacobian Vol ; Integration Int ; }
Galerkin { [ nu[] * br[] , {d a} ] ;
In Vol_Magnet ; Jacobian Vol ; Integration Int ; }
- For i In {1:NumMagnets}
+ For i In {1:NumMagnets}
// dummy term to define dofs for fully fixed space
Galerkin { [ 0 * Dof{un~{i}} , {un~{i}} ] ;
In Vol_Air ; Jacobian Vol ; Integration Int ; }
@@ -301,10 +300,10 @@ Resolution {
PostProcessing {
{ Name MagSta_phi ; NameOfFormulation MagSta_phi ;
Quantity {
- { Name b ;
+ { Name b ;
Value { Local { [ - mu[] * {d phi} ] ; In Dom_Hgrad_phi ; Jacobian Vol ; }
Local { [ - mu[] * hc[] ] ; In Vol_Magnet ; Jacobian Vol ; } } }
- { Name h ;
+ { Name h ;
Value { Local { [ - {d phi} ] ; In Dom_Hgrad_phi ; Jacobian Vol ; } } }
{ Name hc ; Value { Local { [ hc[] ] ; In Vol_Magnet ; Jacobian Vol ; } } }
{ Name phi ; Value { Local { [ {phi} ] ; In Dom_Hgrad_phi ; Jacobian Vol ; } } }
@@ -380,8 +379,7 @@ PostOperation {
SendToServer Sprintf("Output/Magnet %g/Y force [N]", i), Color "Ivory" ];
Print[ fz~{i}[Vol_Air], OnGlobal, Format Table, File > "Fz.dat",
SendToServer Sprintf("Output/Magnet %g/Z force [N]", i), Color "Ivory" ];
- EndFor
+ EndFor
}
}
}
-
diff --git a/Magnetodynamics/transfo.pro b/Magnetodynamics/transfo.pro
index 4e162b010d69bd44351f900ec754fd929a8cebe4..86192e6c81574654c62bd3bda7ecfb3d2d3dfd80 100644
--- a/Magnetodynamics/transfo.pro
+++ b/Magnetodynamics/transfo.pro
@@ -95,6 +95,8 @@ Function {
// secondary.
Flag_CircuitCoupling = 1;
+Flag_FrequencyDomain = 0;
+
// Note that the voltage will not be equally distributed in the PLUS and MINUS
// parts, which is the reason why we must apply the total voltage through a
// circuit -- and we cannot simply use a current source like in Tutorial 7a.
@@ -128,7 +130,7 @@ Function {
// 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;
+ Resistance[R_out] = 10;
// End-winding primary winding resistance for more realistic primary coil
// model