# [Getdp] Magnetodynamics with cohomology conditions

Matti Pellikka matti.pellikka at tut.fi
Wed Aug 14 14:29:28 CEST 2013

```Hello,

Here's a working example based on your .geo-file with both A-V and T-Omega
formulations.

With this geometry, you need one cohomology basis function per inductor
winding, each driven with the same net current. That's essentially the only
change I needed to make to the .pro-file. Note that some of the generated
cohomology basis functions might be oriented to the other direction, which
you can account by driving them by negative current instead.

Another possibility is to model the inductor as a massive conductor. Then,
just one cohomology basis function is needed as there's just one tunnel
through the air region.

--
Matti Pellikka, Researcher, Electromagnetics
Tampere University of Technology, Finland

On 13 August 2013 17:01, Maximilian Szczesliwski <
maximulianszczesliwski at gmail.com> wrote:

> After serveral days of trying to build a similar model like
> "Magnetodynamics with cohomology conditions", I would like to ask you
> kindly for help. Is it possible to calculate only a slice of such a problem
> using cohomology conditions? The goal is to reduce the number of elements
> in piecewise symmetric problems like in an induction heating process with
> several shunts around the inductor.
>
> Please find below my .geo-file.
>
> I would be greatefull for any help.
>
> Maximilian
>
> /*+++++++++++++++++++++++++++++++++++++++++++++
> ++++++++++++  .GEO   +++++++++++
> +++++++++++++++++++++++++++++++++++++++++++++*/
>
>
>
>
> Mesh.Algorithm3D = 4;
> // General.RotationCenterX=270;
> // General.RotationCenterY=0;
> // General.RotationCenterX=360;
> freq=50; // frequenz
> curr=4242*Sqrt(2); // Stromstärke
> eps=1.e-6;
>
> xs1=0.25; // Radius Schmelze unter der Schräge
> xs2=0.325; // großer Radius Schmelze
> y_nenn=1; // Nennhöhe
> ys1=0.180; // höhe der Schräge
>
> wz=1; // windungszahl
> wd=0.004; // windungsabstand
> xw11=xw1+0.00825; // außenradius eckiger teil
> hw=0.0195; // höhe ind
> rw1=0.0065; // innenradius runder teil
> rw2=rw1+0.00325; // außenradius runder teil
> h1=0; // untere Z- Position der ersten Windung
> h2=hw; // obere Z- Position der ersten Windung
> phi=Pi/100; // Rotationswinkel
>
>
>
> Point(1)={0,0 ,0, 0.01};
> Point(2)={xs2,0 ,0, 0.01};
> Point(3)={0,0 ,y_nenn, 0.01};
> Point(4)={xs2,0 ,y_nenn, 0.01};
>
>
>
> // Einsatz
> einsatz_in[]={};
> einsatz_out[]={};
> vol_Einsatz[] = {};
>
> Line(1) = {1,2};
> Line(2) = {2,4};
> Line(3) = {3,4};
> Line(4) = {1,3};
>
> Line Loop(5) = {1,2,-3,-4} ;
> Plane Surface(1) = {5} ;
> tmp[] = {1};
> einsatz_in[]=tmp[0];
>
> tmp[] = Extrude { {0,0,y_nenn}, {0,0,0} ,  phi}{ Surface {tmp[0]}; Layers
> {0.02}; };
> vol_Einsatz[] = tmp[1];
> einsatz_out[]=tmp[0];
>
> // Induktor
> wz=20; // windungszahl
> wd=0.004; // windungsabstand
> xw11=xw1+0.00825; // außenradius eckiger teil
> hw=0.0195; // höhe ind
> rw1=0.0065; // innenradius runder teil
> rw2=rw1+0.00325; // außenradius runder teil
> wg=0;
>
> // coil winding
> in[]={};
> out[]={};
> vol_Induktor[] = {};
> loop[]={};
> For t In {1:wz}
>
> p=newp;
> Point(p+1)={xw1,0 ,wg, 0.005};
> Point(p+2)={xw11,0 ,wg, 0.005};
> Point(p+3)={xw1,0 ,hw+wg, 0.005};
> Point(p+4)={xw11,0 ,hw+wg, 0.005};
>
> l=newl;
> Line(l+1) = {p+1,p+2};
> Line(l+2) = {p+3,p+4};
> Line(l+3) = {p+1,p+3};
> Line(l+4) = {p+2,p+4};
>
> ll=newll;
> Line Loop(ll)={l+1, l+4, -(l+2), -(l+3)};
>
>
> s=news;
>
> Plane Surface(s) = {ll};
> tmp[] = {s};
> in[]+=tmp[0];
>
>
> tmp[] = Extrude { {0,0,y_nenn}, {0,0,0} ,  phi}{ Surface {tmp[0]}; Layers
> {0.02}; };
> vol_Induktor[] += tmp[1];
> out[]+=tmp[0];
>
> wg = t*(hw+wd);
> loop[]+={ll};
> EndFor
>
>
> // Air
> air_in[] = {};
> air_out[] = {};
> vol_air[] = {};
>
> p=newp;
>
> Point(p+1)={0,0 ,-3*y_nenn, 0.5};
> Point(p+2)={4*y_nenn,0 ,-3*y_nenn, 0.5};
> Point(p+3)={0,0 ,4*y_nenn, 0.5};
> Point(p+4)={4*y_nenn,0 ,4*y_nenn, 0.5};
>
> l=newl;
> Line(l+1) = {p+1,p+2};
> Line(l+2) = {p+3,p+4};
> Line(l+3) = {p+1,1};
> Line(l+4) = {3,p+3};
> Line(l+5) = {p+2,p+4};
>
> ll=newll;
> Line Loop(ll)={l+3, 1, 2, -3, l+4, l+2, -(l+5), -(l+1)};
>
> Line Loop(ll+2)={l+3, 4, l+4, l+2, -(l+5), -(l+1)};
> s=news;
> loop[]+=ll;
> Plane Surface(s) = loop[];
>
> tmp[] = {s};
> air_in[]+=tmp[0];
>
> tmp[] = Extrude { {0,0,y_nenn}, {0,0,0} ,  phi}{ Surface {tmp[0]}; Layers
> {0.02}; };
> vol_air[] += tmp[1];
> air_out[]+=tmp[0];
>
> Einsatz = 10000;
> Induktor = 20000;
> Air = 30000;
>
> SKIN_Einsatz = 11000;
> Einsatz_OUT = 12000;
> Einsatz_IN = 13000;
> SKIN_Induktor = 22000;
> OUT = 220000;
> IN = 200002;
> Inf_Air = 33000;
> Air_IN=34000;
> Air_OUT=35000;
>
> Physical Volume(Induktor) = {vol_Induktor[]};
> Physical Volume(Einsatz) = {vol_Einsatz[]};
> Physical Volume(Air) = {vol_air};
>
> Physical Surface(IN)= in[];
> Physical Surface(OUT)= out[];
> skin_induktor[]={};
> skin_induktor[]=CombinedBoundary{ Volume{vol_Induktor[]}; };
> skin_induktor[] -= {in[], out[]};
> Physical Surface(SKIN_Induktor) = skin_induktor[];
> skin_einsatz[] = {};
> skin_einsatz[] = Boundary { Volume{vol_Einsatz[]}; };
> skin_einsatz[] -= {einsatz_in[], einsatz_out[]};
> Physical Surface(Einsatz_IN)= einsatz_in[];
> Physical Surface(Einsatz_OUT)= einsatz_out[];
> Physical Surface(SKIN_Einsatz) = skin_einsatz[];
>
> Physical Line(999999) = {84,4, 85};
> // axis[]={56, 4, 55};
> Physical Surface(Inf_Air) = {90, 97, 93}; // , 61, 113};
>
>
>
>
> Physical Surface(Air_IN)= air_in[];
> Physical Surface(Air_OUT)= air_out[];
>
> // Cohomology computation for the A-V method
> Cohomology(1) {{Induktor},{IN,OUT}};
> Cohomology(1) {{Einsatz,},{Einsatz_IN,Einsatz_OUT}};
>
> _______________________________________________
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> getdp at geuz.org
> http://www.geuz.org/mailman/listinfo/getdp
>
>
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```