I'm trying to solve a stokes system with some funny boundary conditions
so I've stripped the code to make sure I was getting the correct answers
to a very simple system as follows:
governing equations are:
div grad u + grad p = f
div u = 0
i'm setting u=0 on the boundaries, giving u=0 (or close enough) everywhere.
setting f = -(0,1), i should get a linear profile with pressure
increasing with depth at the same rate going downwards.
Yes. But if you impose Dirichlet boundary values for the velocity all
around the boundary, then the pressure is only determined up to a
constant, i.e., the pressure should be a linear function but the offset
is not determined by the equation.
I'm clearly not understanding how to use
VectorTools::interpolate_boundary_values correctly, and I would
appreciate some clarification on it.
I'm imposing a zero pressure at the top of my rectangle with height of
10, which means I should get 10 at the bottom for pressure.
You can't do that. If you have Dirichlet boundary conditions for the
velocity, then you can't impose anything on the pressure. In fact, for
the incompressible Stokes equations, you can never impose any pressure
boundary conditions.
There is a description of boundary conditions for the Stokes equations
in the introduction of step-22. Take a look there to see what you can
and cannot impose for the Stokes equations.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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