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## Re: [ff3d-users] Could you help me confirm a time-dependent PDE?

 From: Stephane Del Pino Subject: Re: [ff3d-users] Could you help me confirm a time-dependent PDE? Date: Wed, 25 Feb 2004 17:50:43 +0100 User-agent: KMail/1.5.4

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On Wednesday 25 February 2004 00:20, Robert Li wrote:
> Dear Stephane Del Pino,
>
>   I tested ff3d with a realistic thermal PDE. However,
> I found that the result of ff3d was different from
> that of SVHEAT and TEMP/W, which are also FEM solution
> software. But the other two have close result, or
> almost same.
>
>   I am not sure about how to write PDE in input file.
> For example, It seems that -div((f2)*grad(T)) = 0; and
> -div((f2)*grad(T)) = 0; are different. But I don't
> know why?

You probably made a mistake writing the mail, the two formulae are the
same ... Could you give more details, please?

>  Could you help me confirm the following
> time-dependent PDE?
>
> 1.Real Heat flow Equation
> dx(Kx*dx(T)) + dy(Ky*dy(T)) +
> dz(Kz*dz(T))=(Cp+Lf*Theat*Theatu1)*(dt(T))
> where, T=Temperature,
> dt=time
> 2.I expressed it in ff3d input file as follows:
>
I think that this last equation is not equivalent to the first one.
Let me explain which mistake I think you did:

you want to solve something like
Using an Euler implicite scheme, the time discretization is:
The this is *not* equivalent to
Since a(x) cannot go inside the divergence term. A correct way of doing it
could be:

Please tell me if that helps.

Best regards,
Stephane.
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