[Getdp] Coupling Analysis (Thermo MagDyn)
ABE Hiroshi
habe36 at gmail.com
Wed Oct 18 16:14:06 CEST 2017
Dear Prof. Sabariego and All,
I looked into the new indheat.pro benchmark and change several lines to use AV formulation, MagDynAV formulation.
The diff file is this.
325c325,326
< { Name h; Type Local; NameOfSpace HSpace; }
---
> { Name a; Type Local; NameOfSpace ASpace; }
> { Name e; Type Local; NameOfSpace ESpace; }
333c334
< Galerkin { [ -0.5/sigma[]*<h>[Re[{d h}]*Re[{d h}] + Im[{d h}]*Im[{d h}]], {t} ];
---
> Galerkin { [ -0.5/sigma[]*<a>[Re[Dt[-{a}]+{e}]*Re[Dt[-{a}]+{e}] + Im[Dt[-{a}]+{e}]*Im[Dt[-{a}]+{e}]], {t} ];
378c379
< { Name A; NameOfFormulation MagDynTO;
---
> { Name A; NameOfFormulation MagDynAV;
478c479
< { Name p; Value{ Local{ [ 1./sigma[]*( Re[{d h}]*Re[{d h}] + Im[{d h}]*Im[{d h}] ) ] ;
---
> { Name p; Value{ Local{ [ -0.5/sigma[]*<a>[Re[Dt[-{a}]+{e}]*Re[Dt[-{a}]+{e}] + Im[Dt[-{a}]+{e}]*Im[Dt[-{a}]+{e}]] ] ;
The simulation results are very different from the original TO formulation.
My concerning points are
* In AV formulation, “a" and “e" are both complex numbers so <a>[] should be something like <a,e>[].
* The operator “Dt” would work as expected in the TheDyn formulation, it is transient formulation.
I tried <a,e>[], but this causes a syntax error.
I have a feeling I am closing to my goal. I appreciate your kind helps.
Thank you very much in advance.
Best Regards,
2017/10/18 0:04、Ruth Vazquez Sabariego <ruth.sabariego at kuleuven.be> のメール：
> Dear ABE Hiroshi,
>
> Using the T-O or the A-V formulation is just a choice, that most of the time depends on the data we have.
> Refining the mesh, you should observe convergence of the results.
>
> As you’ve done, the coupling between the EM and the thermal problem is done via the Joule losses.
> These losses are calculated from the frequency domain solution (steady state) of the AV-formulation, and therefore they are an average value.
> The thermal problem is then solve in the time domain. This is possible thanks to the difference in time constants of both problems.
>
> The coupling term can be written as:
>
> Galerkin { [ -0.5*sigma[] *<a>[ SquNorm[Dt[{a}]+{d v}] ], {t} ];
> In DomainC; Integration II; Jacobian Vol; }
>
> where <a> indicates that the operation between square brackets is to be done with complex numbers even if the thermal formulation is real.
>
> This term is exactly the same as yours (with a factor 0.5, that I think is missing, to check!) if you also indicate there that the quantities are complex, i.e.
>> Galerkin { [ -1./sigma[]*( <a>[
>> Re[-(Dt[{a}]+{d v})]*
>> Re[-(Dt[{a}]+{d v})]+
>> Im[-(Dt[{a}]+{d v})]*
>> Im[-(Dt[{a}]+{d v})]] ), {t} ];
>> In DomainC; Integration II; Jacobian Vol; }
>
>
> If you do not indicate that the quantities are complex, the imaginary part is disregarded in the time domain thermal formulation.
>
> Regards,
> Ruth
>
> PS: I am correcting the formulation in the benchmarks.
>
>
> —
> Prof. Ruth V. Sabariego
> KU Leuven
> Dept. Electrical Engineering ESAT/Electa, EnergyVille
> http://www.esat.kuleuven.be/electa
> http://www.energyville.be
>
> Free software: http://gmsh.info | http://getdp.info | http://onelab.info
>
>
>
>
>
>
>
>> On 17 Oct 2017, at 11:04, ABE Hiroshi <habe36 at gmail.com> wrote:
>>
>> Dear All,
>>
>> I am working on a coupling analysis of magnetodynamics and thermal dynamics. Referring to “indheat” sample, I build a model.
>> It uses A-V formulation regarding Magnetodynamics, and I would like to couple the electric current in the thermal formulation.
>>
>> They are:
>>
>> Formulation {
>>
>> { Name MagStaDyn_av_js0_3D ; Type FemEquation ;
>> Quantity {
>> { Name a ; Type Local ; NameOfSpace HSpace ; }
>> { Name v ; Type Local ; NameOfSpace USpace ; }
>> }
>>
>> Equation {
>> Galerkin { [ nu[] * Dof{d a} , {d a} ] ;
>> In Domain ; Jacobian Vol ; Integration II ; }
>> Galerkin { DtDof[ sigma[] * Dof{a} , {a} ] ;
>> In DomainC ; Jacobian Vol ; Integration II ; }
>> Galerkin { [ sigma[] * Dof{d v} , {a} ] ;
>> In DomainC ; Jacobian Vol ; Integration II ; }
>>
>> Galerkin { [ -js0[], {a} ] ;
>> In DomainS ; Jacobian Vol ; Integration II ; }
>>
>>
>> Galerkin{ DtDof[ sigma[] * Dof{a}, {d v} ] ;
>> In DomainC ; Jacobian Vol ; Integration II ; }
>> Galerkin{ [ sigma[] * Dof{d v} , {d v} ] ;
>> In DomainC ; Jacobian Vol ; Integration II ; }
>>
>> }
>> }
>>
>> { Name Thermal; Type FemEquation;
>> Quantity {
>> { Name t; Type Local; NameOfSpace TSpace; }
>> { Name a; Type Local; NameOfSpace HSpace; }
>> { Name v; Type Local; NameOfSpace USpace; }
>> }
>> Equation {
>> Galerkin { [ K[] * Dof{d t}, {d t} ];
>> In DomainC; Integration II; Jacobian Vol; }
>> Galerkin { DtDof [ rho[]*Cp[] * Dof{t}, {t} ];
>> In DomainC; Integration II; Jacobian Vol; }
>> Galerkin { [ -1./sigma[]*(
>> Re[-(Dt[{a}]+{d v})]*
>> Re[-(Dt[{a}]+{d v})]+
>> Im[-(Dt[{a}]+{d v})]*
>> Im[-(Dt[{a}]+{d v})]), {t} ];
>> In DomainC; Integration II; Jacobian Vol; }
>>
>> Galerkin { [ Ht[]*Dof{t}, {t} ];
>> In Skin_ECore; Jacobian Sur ; Integration II ; }
>> Galerkin { [-Ht[]*Tamb[], {t} ];
>> In Skin_ECore; Jacobian Sur ; Integration II ; }
>> Galerkin { [ sigma_sb*Ep[]*(Dof{t})^4, {t} ];
>> In Skin_ECore; Jacobian Sur ; Integration II ; }
>> Galerkin { [ -sigma_sb*Ep[]*(Tamb[])^4, {t} ];
>> In Skin_ECore; Jacobian Sur ; Integration II ; }
>>
>> }
>> }
>> }
>>
>> The MagStaDyn_av_js0_3D formulation gives a resonable solution but Thermal gives weird results.
>>
>> I know the “indheat” example uses T-O formulation for coupling analysis. Are there any reasons to take T-O formulation instead of A-V formulation?
>> Any ways for A-V formulation?
>>
>> Thank you so much.
>>
>> Best,
>>
>> ABE Hiroshi
>> from Tokorozawa, JAPAN
>>
>>
>> _______________________________________________
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>
ABE Hiroshi
from Tokorozawa, JAPAN
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