Thank you for your reply. My interface condition is \integral_{Interface}
p*I*n_stokes - jump(velocity_gradient) ds,
Do you really mean that the *integral* is zero, or should this hold pointwise?
Either way, I am pretty sure that you can't expect this to be true pointwise
for the discrete solution. Furthermore, what it really says is *not* that the
velocity gradient must be continuous, but that the gradient has a jump equal
to the pressure times the normal vector. So a method that guarantees a C^1
solution would not actually help you.
where I is the interface and
jump(velocity_gradient) = vel_grad_stokes*n_stokes +
vel_grad_laplace*n_laplace. I am using this with zero boundary conditions on
pressure. The interface in the code I attached is y=0.5, with y>=0.5 stokes
and below y=0.5 laplace. When I let the mesh size go to zero, even when I
prescribe zero pressure everywhere (by defining zero contribution from
pressure on my right hand side) I am still not getting zero pressure as the
mesh size goes to zero. Furthermore, as my mesh size goes to zero my velocity
converges to something that is not related to the right-hand side I chose.
Specifically, it feautures a non zero jump in the gradient across the
interface, even though I am prescribing the same right-hand side to both sides
(i.e. with zero pressure on both sides). This does not happen if I solve just
stokes everywhere or just laplace (with the same right hand side :i.e. zero
contribution from pressure).
I don't have a suggestion here other than simplifying the problem and spending
some time gathering other cues. Does the code work if one or the other medium
makes up the whole domain?
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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