[petsc-users] Scalable Solver for Incompressible Flow

[Jed Brown]

Sebastian Blauth <sebastian.blauth at itwm.fraunhofer.de> writes:

> I agree with your comment for the Stokes equations - for these, I have 
> already tried and used the pressure mass matrix as part of a (additive) 
> block preconditioner and it gave mesh independent results.
>
> However, for the Navier Stokes equations, is the Schur complement really 
> spectrally equivalent to the pressure mass matrix? 

No, it's not. You'd want something like PCD (better, but not algebraic) or LSC.

> And even if it is, the convergence is only good for small Reynolds numbers, for moderately high ones the convergence really deteriorates. This is why I am trying to make fieldsplit_schur_precondition selfp work better (this is, if I understand it correctly, a SIMPLE type preconditioner).

SIMPLE is for short time steps (not too far from resolving CFL) and bad for steady. This taxonomy is useful, though the problems are super academic and they don't use high aspect ratio.

https://doi.org/10.1016/j.jcp.2007.09.026