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Re: [ff3d-users] Variational form of potential flow with free surface on


From: Stephane Del Pino
Subject: Re: [ff3d-users] Variational form of potential flow with free surface on mesh
Date: Sat, 17 May 2008 09:04:10 +0200
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Dear Thomas,
thanks for your interest in ff3d.

In fact, you did not compute the right variational formulation associated to 
your PDE. You have to be careful in the integration by part

Have a look to
http://en.wikipedia.org/wiki/Finite_element_method#Variational_formulation
and to
http://en.wikipedia.org/wiki/Green%27s_identities
for some details.

In your case, you should have written:

 solve(phi) in  M
 {
    test(w)
      int(grad(phi)*grad(w))
      +int[M zmax](w*alpha*phi)
      =int[M xmin](w*f)
      -int[M xmax](w*f)
      =0;
 };

Do not hesitate to ask me if you get troubles with that.

> PS
> One small documentation suggestion; the method of defining Robin type
> boundary conditions be added to the documentation or README file.
The documentation is far from being completed. I not this on the TODO list.

Best regards,
St├ęphane.




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