Navier Stokes demo

On 17 March 2013 22:50, Peter Franek
<email address hidden>wrote:

> New question #224508 on FEniCS Project:
> https://answers.launchpad.net/fenics/+question/224508
>
> I have a math question about the Navier-Stokes demo. It uses the Chorin
> projection method and in the second step, the new pressure is computed from
> the tentative velocity. The problem to be solved at this step is laplace
> p=(grad u*)/k_n. So, in the variational formulation I would expect
> something like
>
> -<grad p, grad q>+integral over boundary from (q times normal derivative
> of p) = rhs
>
> However, in the implementation, this "boundary integral" is missing. If
> the variational problem is satisfied for all q in the demo, than it implies
> a boundary condition \partial_n p=0 everywhere on the boundary. However, in
> addition to this, the line
> [bc.apply(A2, b2) for bc in bcp] ...
> seems to require also a dirichlet boundary condition at the inflow and
> outflow. Aren't here too many boundary conditions on p?
>
> Thanks for an explanation and sorry if I misunderstood something. Peter
>

The splitting scheme requires that you set boundary conditions everywhere
for both velocity
and pressure, in contrast to the Navier-Stokes equations themselves that
require one less condition.
For Neumann conditions, nu du/dn - pn = g , it is common to translate this
condition into
a Neumann condition for the velocity and a Dirichlet condition for the
pressure, which should add up to g.
Dirichlet conditions translates to Dirichlet for the velocity and Neumann
for the pressure.

Kent

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Hello, let me put my question more clearly. In the current implementation of the pressure-calculation step (A2, b2), the calculated pressure does, or does not satisfy a von Neuman condition "normal derivative of p is zero everywhere on the boundary"? Thanks a lot.

Thanks Kent-Andre Mardal, that solved my question.