Dear Prof. Bangerth,
Thank you very much for your reply! Apologies for the ambiguity. What I
meant is for the interface condition to hold weakly on the boundary and
that, as you correctly pointed out, the jump in the gradient should equal
the pressure times the normal vector. As such, I specified a pressure
which I know integrates to zero on the interface, and since my velocity is
the same expression on either side of the interface I would expect it to
integrate to zero too. When I run the code by specifying the same model
over the whole domain I get what I would expect. When I allow for the
interface then the pressure shoots off to infinity at the intersection of
the interface and the boundary (where I specify homogeneous dirichlet for
the velocity). I then also get an unexpected non-zero jump in the pressure
gradient. I am currently trying to work around that issue.
Kind regards,
Georgios
On Thursday, August 23, 2018 at 9:27:12 PM UTC+1, Wolfgang Bangerth wrote:
>
>
> > 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.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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