pp

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
     }
   }
 }
-

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