[petsc-users] Scalable Solver for Incompressible Flow

[Alexander Lindsay]

This has been a great discussion to follow. Regarding

> when time stepping, you have enough mass matrix that cheaper
preconditioners are good enough

I'm curious what some algebraic recommendations might be for high Re in
transients. I've found one-level DD to be ineffective when applied
monolithically or to the momentum block of a split, as it scales with the
mesh size. For high Re boomeramg is ineffective perhaps until
https://gitlab.com/petsc/petsc/-/issues/1362 is resolved. I should try
fiddling around again with Pierre's work in HPDDM, but curious if there are
other PETSc PC recs, or if I need to overcome my inertia/laziness and move
beyond command line options.

On Mon, May 8, 2023 at 6:46 AM Jed Brown <jed at jedbrown.org> wrote:

> Sebastian Blauth <sebastian.blauth at itwm.fraunhofer.de> writes:
>
> > Hello everyone,
> >
> > I wanted to briefly follow up on my question (see my last reply).
> > Does anyone know / have an idea why the LSC preconditioner in PETSc does
> > not seem to scale well with the problem size (the outer fgmres solver I
> > am using nearly scale nearly linearly with the problem size in my
> example).
>
> The implementation was tested on heterogeneous Stokes problems from
> geodynamics, and perhaps not on NS (or not with the discretization you're
> using).
>
> https://doi.org/10.1016/j.pepi.2008.07.036
>
> There is a comment about not having plumbing to provide a mass matrix. A
> few lines earlier there is code using PetscObjectQuery, and that same
> pattern could be applied for the mass matrix. If you're on a roughly
> uniform mesh, including the mass scaling will probably have little effect,
> but it could have a big impact in the presence of highly anistropic
> elements or a broad range of scales.
>
> I don't think LSC has gotten a lot of use since everyone I know who tried
> it has been sort of disappointed relative to other methods (e.g., inverse
> viscosity scaled mass matrix for heterogeneous Stokes, PCD for moderate Re
> Navier-Stokes). Of course there are no steady solutions to high Re so you
> either have a turbulence model or are time stepping. I'm not aware of work
> with LSC with turbulence models, and when time stepping, you have enough
> mass matrix that cheaper preconditioners are good enough. That said, it
> would be a great contribution to support this scaling.
>
> > I have also already tried using -ksp_diagonal_scale but the results are
> > identical.
>
> That's expected, and likely to mess up some MG implementations so I
> wouldn't recommend it.
>
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