[Getdp] Coupling Analysis (Thermo MagDyn)

[Ruth Vazquez Sabariego]

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

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On 17 Oct 2017, at 11:04, ABE Hiroshi <habe36 at gmail.com<mailto: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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