[petsc-users] Scalable Solver for Incompressible Flow

[Matthew Knepley]

On Tue, May 2, 2023 at 2:29 PM Jed Brown <jed at jedbrown.org> wrote:

> 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.
>

I think you can do a better job than that using something like

  https://arxiv.org/abs/1810.03315

Basically, you use an augmented Lagrangian thing to make the Schur
complement well-conditioned,
and then use a special smoother to handle that perturbation.


> > 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
>

   Thanks,

      Matt

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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