Re: [ff3d-users] Code to solve Fick's law, what's wrong??!!

[Stephane Del Pino]

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Hello Arun.

Le samedi 15 Mai 2004 17:24, Arun Viswanathan a écrit :
> Hey Stephane,
>
> I am so sorry to be bothering you so often, the whole
> thing is new to me, that's why I have too many
> doubts....here's yet another...:)...
>
> In the example of the Euler's equation that you sent
> me, 'dt' is simply declared as any other variable. In
> my equation of Fick's law, I don't think I can do
> that. The equation I am trying to solve goes this way:
No. This example does not deal with Euler's equations but is an implicit Euler 
*scheme* wrote to solve your problem.

As it is the case in every freefem version, functions do not depend on time, 
only on space. But this is not a problem.

> d/dt [C(x,t)] = D * d^2/dx [C(x,t)]
In ff3d, to solve this problem the spacial discretization is done 
independently. So, to solve
        d/dt(u)-div(D*grad(u)) = 0,
an implicit Euler scheme consists in writing 
        (u(n+1)-u(n))/delta_t - div(D*grad(u(n+1))) = 0,
where n is the time step.
For convenience, this can be written:
        u(n+1)-div(D*delta_t*grad(u(n+1)))=u(n).

This is exactly what solves the programm that I sent to you.

I hope that it is now more clear.
Best regards,
Stephane.

PS : please do not cross post your requests. This is not related with the -dev 
mailing list and I read more often the -users mailing list that this 
personnal address (address@hidden).
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