[Getdp] Thermal - Convection Formulation
mkoch at gvtc.com
mkoch at gvtc.com
Wed Mar 15 16:55:04 CET 2006
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
>
>
>
>
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