I want to verify a finite-volume solver (SIMPLE-Algorithm) for the incompressible Navier-Stokes equations by using a manufactured solution. I use Dirichlet boundary conditions for the velocity at all boundaries. The manufactured solution for the velocities I use, is constructed as the curl of a vector field and thereby fulfills the continuity equation at any point.
Depending on how I choose the domain on which to solve the equations I run into convergence problems: The residual of the pressure correction equation stagnates after an initial decrease.
I am approximating the mass fluxes through boundary faces using the midpoint rule and apparently this leads to a net loss/gain of mass considering the entire problem domain.
Is this the normal behavior? Are there any remedies other than choosing a manufactured solution that identically vanishes at the boundaries? Would it be an option to provide the exact mass flux instead of the approximate (not sure if this is allowed, since the Dirichlet boundary condition only fixes the velocity)?