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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: Tue, 20 May 2008 01:31:39 +0200 User-agent: KMail/1.9.9

```Hello Thomas.

Le Sunday 18 May 2008, Thomas Ward a écrit :
> 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.
It is not equivalent. I join you a formal way of getting this variationnal
formula.  Check finite element books to get details and a clean establishment
of the formula.

> 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?
Yes this is not a big deal in ff3d. Assume that M is your structured mesh,
then
M = periodic(M,0:1,2:3,4:5);
will create a triperiodic mesh where
0 represents xmin,
1 represents xmax,
2 represents ymin,
3 represents ymax,
4 represents zmin,
5 represents zmax,

M = periodic(M,2:3);
would create a periodic mesh in the direction y. Note that up to now M must be
a structured mesh.

> Do you have any infinite elements? I'm thinking of a radiation condition
> decaying to zero at infinity on an open boundary.
No. No such element is implemented ...

Best regards,
Stéphane.
```

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