[petsc-users] Penalization vs. setting interior points for Laplace eqn

[Åsmund Ervik]

Dear PETSc users,

(This may not be very PETSc-specific, but here goes.)

I'm using KSP for solving two equations of Poisson/Laplace type. First I solve a Laplace equation in a box with Dirichlet BCs on the top/bottom and Neumann on the sides, and discontinuous coefficients inside the box. This gives me an electric potential. I then use this as one input in a two-phase incompressible Navier-Stokes solver in the same box domain, again with discontinuous coefficients, where the electric potential contributes to part of the pressure jump across the phase boundaries. Here I solve a pressure Poisson equation. This code gives good results which agree with theoretical results and experiments.

Now I want to do simulations in a complex domain. I have already implemented L2 penalization for the flow part, without an electric field, and this works well. Now I want to be able to set a constant potential in the part of the domain where I apply penalization. Does it make sense to do penalization for the Laplace equation somehow, or should I just set the potential values on the grid points where I want to?

Regards,
Åsmund