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

[Thomas Ward]

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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