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<div class="">Dear ABE Hiroshi, </div>
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<div class="">Using the T-O or the A-V formulation is just a choice, that most of the time depends on the data we have. </div>
<div class="">Refining the mesh, you should observe convergence of the results.</div>
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<div class="">As you’ve done, the coupling between the EM and the thermal problem is done via the Joule losses. </div>
<div class="">These losses are calculated from the frequency domain solution (steady state) of the AV-formulation, and therefore they are an average value.</div>
<div class="">The thermal problem is then solve in the time domain. This is possible thanks to the difference in time constants of both problems. </div>
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</div>
<div class="">The coupling term can be written as:</div>
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<div class="">Galerkin { [ -0.5*sigma[] *<a>[ SquNorm[Dt[{a}]+{d v}] ], {t} ];</div>
<div class=""> In DomainC; Integration II; Jacobian Vol; }</div>
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</div>
<div class="">where <a> indicates that the operation between square brackets is to be done with complex numbers even if the thermal formulation is real.</div>
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<div class="">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.</div>
<div class="">
<blockquote type="cite" class="">Galerkin { [ -1./sigma[]*( <a>[ <br class="">
<span class="Apple-tab-span" style="white-space: pre;"></span> Re[-(Dt[{a}]+{d v})]*<br class="">
<span class="Apple-tab-span" style="white-space: pre;"></span> Re[-(Dt[{a}]+{d v})]+<br class="">
<span class="Apple-tab-span" style="white-space: pre;"></span> Im[-(Dt[{a}]+{d v})]*<br class="">
<span class="Apple-tab-span" style="white-space: pre;"></span> Im[-(Dt[{a}]+{d v})]] ), {t} ];<br class="">
<span class="Apple-tab-span" style="white-space: pre;"></span>In DomainC; Integration II; Jacobian Vol; }</blockquote>
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<div class="">If you do not indicate that the quantities are complex, the imaginary part is disregarded in the time domain thermal formulation. </div>
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<div class="">Regards, </div>
<div class="">Ruth</div>
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</div>
<div class="">PS: I am correcting the formulation in the benchmarks. </div>
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<div class="">
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—<br class="">
Prof. Ruth V. Sabariego<br class="">
KU Leuven <br class="">
Dept. Electrical Engineering ESAT/Electa, EnergyVille<br class="">
<a href="http://www.esat.kuleuven.be/electa" class="">http://www.esat.kuleuven.be/electa</a></div>
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<blockquote type="cite" class="">
<div class="">On 17 Oct 2017, at 11:04, ABE Hiroshi <<a href="mailto:habe36@gmail.com" class="">habe36@gmail.com</a>> wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div class="">Dear All,<br class="">
<br class="">
I am working on a coupling analysis of magnetodynamics and thermal dynamics. Referring to “indheat” sample, I build a model.<br class="">
It uses A-V formulation regarding Magnetodynamics, and I would like to couple the electric current in the thermal formulation.<br class="">
<br class="">
They are:<br class="">
<br class="">
Formulation {<br class="">
<br class="">
{ Name MagStaDyn_av_js0_3D ; Type FemEquation ;<br class="">
Quantity {<br class="">
{ Name a ; Type Local ; NameOfSpace HSpace ; }<br class="">
{ Name v ; Type Local ; NameOfSpace USpace ; }<br class="">
}<br class="">
<br class="">
Equation {<br class="">
Galerkin { [ nu[] * Dof{d a} , {d a} ] ;<br class="">
In Domain ; Jacobian Vol ; Integration II ; }<br class="">
Galerkin { DtDof[ sigma[] * Dof{a} , {a} ] ;<br class="">
In DomainC ; Jacobian Vol ; Integration II ; }<br class="">
Galerkin { [ sigma[] * Dof{d v} , {a} ] ;<br class="">
In DomainC ; Jacobian Vol ; Integration II ; }<br class="">
<br class="">
Galerkin { [ -js0[], {a} ] ;<br class="">
In DomainS ; Jacobian Vol ; Integration II ; }<br class="">
<br class="">
<br class="">
Galerkin{ DtDof[ sigma[] * Dof{a}, {d v} ] ;<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In DomainC ; Jacobian Vol ; Integration II ; }<br class="">
Galerkin{ [ sigma[] * Dof{d v} , {d v} ] ;<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In DomainC ; Jacobian Vol ; Integration II ; }<br class="">
<br class="">
}<br class="">
}<br class="">
<br class="">
{ Name Thermal; Type FemEquation;<br class="">
Quantity {<br class="">
{ Name t; Type Local; NameOfSpace TSpace; }<br class="">
{ Name a; Type Local; NameOfSpace HSpace; }<br class="">
{ Name v; Type Local; NameOfSpace USpace; }<br class="">
}<br class="">
Equation {<br class="">
Galerkin { [ K[] * Dof{d t}, {d t} ];<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In DomainC; Integration II; Jacobian Vol; }<br class="">
Galerkin { DtDof [ rho[]*Cp[] * Dof{t}, {t} ];<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In DomainC; Integration II; Jacobian Vol; }<br class="">
Galerkin { [ -1./sigma[]*( <br class="">
<span class="Apple-tab-span" style="white-space:pre"></span> Re[-(Dt[{a}]+{d v})]*<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span> Re[-(Dt[{a}]+{d v})]+<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span> Im[-(Dt[{a}]+{d v})]*<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span> Im[-(Dt[{a}]+{d v})]), {t} ];<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In DomainC; Integration II; Jacobian Vol; }<br class="">
<br class="">
Galerkin { [ Ht[]*Dof{t}, {t} ];<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In Skin_ECore; Jacobian Sur ; Integration II ; }<br class="">
Galerkin { [-Ht[]*Tamb[], {t} ];<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In Skin_ECore; Jacobian Sur ; Integration II ; }<br class="">
Galerkin { [ sigma_sb*Ep[]*(Dof{t})^4, {t} ];<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In Skin_ECore; Jacobian Sur ; Integration II ; }<br class="">
Galerkin { [ -sigma_sb*Ep[]*(Tamb[])^4, {t} ];<br class="">
<span class="Apple-tab-span" style="white-space:pre"></span>In Skin_ECore; Jacobian Sur ; Integration II ; }<br class="">
<br class="">
}<br class="">
}<br class="">
}<br class="">
<br class="">
The MagStaDyn_av_js0_3D formulation gives a resonable solution but Thermal gives weird results.<br class="">
<br class="">
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?<br class="">
Any ways for A-V formulation?<br class="">
<br class="">
Thank you so much.<br class="">
<br class="">
Best,<br class="">
<br class="">
ABE Hiroshi<br class="">
from Tokorozawa, JAPAN<br class="">
<br class="">
<br class="">
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