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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: Tue, 20 May 2008 11:55:28 +0100 User-agent: Thunderbird 2.0.0.14 (X11/20080505)

```Many thanks Stephane, I think I have got it now.

```
we choose test_fn_boundary = -test_fn_volume so that after integrating the volume integral of test_fn_volume x div(grad(phi) by parts the surface integral terms cancel out with Neumann terms of the test_fn_boundary x boundary conditions integral.
```

```
I hope to try the periodic conditions next week, its not totally clear to me how the periodic mesh becomes a periodic boundary condition but I will have a try first and then ask if I can't work it out.
```

Tom

Stephane Del Pino wrote:
```
```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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