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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 (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.


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,


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