[Getdp] Thermal - Convection Formulation

[mkoch at gvtc.com]

Hi Laird,

the use of T rather than Dof{T} in the radiation term of the 
formulation, as was
explained to me by Christophe, has to do with the fact that only linear terms
should be used with Dof, and Dof{T}^4 would be non-linear. Using T instead of
Dof{T} means using the result of the previous timestep (or previous iteration,
I suppose).

I guess one could linearize the Dof{T}^4 term around Dof{T}, e.g. by writing
Dof{T} = T0 + dT and then, using (1+e)^4 = 1+4e with e = dT/T0, Dof{T}^4 =
4*Dof{T}*T0^3 - 3*To^4, although I am not sure this would satisfy the 
linearity
requirement, either.

The use of two lines for the convection term rather than one line may have a
similar reason, i.e. the Dof{T} somehow needs to stand on its own. I do 
seem to
recall, though, that I was able to use a single line formulation here a while
back - I'll go back and check.

I am by no means an expert on GetDP, but since I have been here before, I
thought I'd take a little load off of Christophe. I do use GetDP in thermal
calculations, however.

Regards,

Matt Koch, Ph.D., P.E.
Science & Technology Consultants (SciTeX)
978-726-4202
mattkoch at scitex.us
www.scitex.us


----- Message from lbolt1 at irf.com ---------
    Date: Wed, 15 Mar 2006 05:37:14 -0800
    From: Laird Bolt <lbolt1 at irf.com>
Reply-To: Laird Bolt <lbolt1 at irf.com>
Subject: [Getdp] Thermal - Convection Formulation
      To: getdp at geuz.org


> Hello:
>
> Would it be possible for someone on the list to please explain why 
> the following two
> formulations are not the same (or to point me to specific reference 
> that explains it)?
>
> Formulation for Convection BC that works (last two Galerkin terms);
>
>    Equation {
>      Galerkin { [ k[] * Dof{d T} , {d T} ];
>                 In Vol_The; Integration I1; Jacobian JVol;  }
>      Galerkin { [ -Flux[] , {T} ]; // - sign for incoming flux
>                 In FluxIn; Integration I1; Jacobian JSur;  }
>      Galerkin { [ alpha[] * Dof{T} , {T} ];
>                 In Convection; Integration I1; Jacobian JSur;  }
>      Galerkin { [ -alpha[] * 348 , {T} ];
>                 In Convection; Integration I1; Jacobian JSur;  }
>    }
>
>
>
> Formulation for Convection that did not work (last Galerkin term)
>
>    Equation {
>      Galerkin { [ k[] * Dof{d T} , {d T} ];
>                 In Vol_The; Integration I1; Jacobian JVol;  }
>      Galerkin { [ -Flux[] , {T} ]; // - sign for incoming flux
>                 In FluxIn; Integration I1; Jacobian JSur;  }
>      Galerkin { [ alpha[] * (Dof{T} - 348) , {T} ];
>                 In Convection; Integration I1; Jacobian JSur;  }
>    }
>
> Also:
>
> Could someone please help me out by explaining why in the Thermal 
> example on Wiki the last
> Galerkin Term (Radiated losses) does not require the use of Dof but 
> the other terms that use
> {T} do require it.
>
>> From Thermal.pro
>
>      Galerkin { [ k[] * Dof{d T} , {d T} ];
>                 In Vol_The; Integration I1; Jacobian JVol;  }
>
>      Galerkin { Dt [ rhoc[] * Dof{T} , {T} ];
>                 In Vol_The; Integration I1; Jacobian JVol;  }
>
>      Galerkin { [ -qVol[] , {T} ];
>                 In Vol_The; Integration I1; Jacobian JVol;  }
>
>      Galerkin { [ -Flux[] , {T} ]; // - sign for incoming flux
>                 In Sur_The; Integration I1; Jacobian JSur;  }
>
>      Galerkin { [ h[] * Dof{T} , {T} ] ;
>                 In SurConv_The ; Integration I1; Jacobian JSur;  }
>
>      Galerkin { [ -h[] * TConv[] , {T} ] ;
>                 In SurConv_The ; Integration I1; Jacobian JSur;  }
>
>      Galerkin { [ hr[{T}] * (({T}+273.)^4-(TConv[]+273.)^4) , {T} ] ;
>                 In SurRad_The ; Integration I1; Jacobian JSur;  }
>
>
> Thankyou
>
> Laird Bolt
>
>
>
>


----- End message from lbolt1 at irf.com -----



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