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


From: Thomas Ward
Subject: Re: [ff3d-users] Variational form of potential flow with free surface on mesh
Date: Sun, 18 May 2008 10:49:14 +0100
User-agent: Thunderbird 2.0.0.14 (X11/20080505)

Thanks Stephane, that fixed it.

I thought my formulation was equivalent to the one you wrote,

As I understand it, my formulation includes the natural boundary conditions which is unnecessary but I thought that there was no harm (other than inefficiency) to include them, anyway thanks for the pointers to the wikipedia stuff, I will look through them and try to see why including the natural boundary codtions in the surface integral won't work.


I'm about to try using periodic BC, I note from the mailing list that you were playing around with this a couple of years ago, do you have any sample files or other documentation or pointers to the source code?

Do you have any infinite elements? I'm thinking of a radiation condition decaying to zero at infinity on an open boundary.

regards,

Tom

Stephane Del Pino wrote:
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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