[Getdp] Coupling Analysis (Thermo MagDyn)

[ABE Hiroshi]

Dear Prof Sabariego,

Thank you for your very helpful information, <a> function.

Also I got the situation on the detail of the formulation.
I’ll try further on my application.

Best,

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. 
> 
> 
>> 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.
>> 

ABE Hiroshi
 from Tokorozawa, JAPAN

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