[petsc-users] Scalable Solver for Incompressible Flow

[Jed Brown]

Alexander Lindsay <alexlindsay239 at gmail.com> writes:

> 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. 

What mesh aspect ratio and streamline CFL number? Assuming your model is turbulent, can you say anything about momentum thickness Reynolds number Re_θ? What is your wall normal spacing in plus units? (Wall resolved or wall modeled?)

And to confirm, are you doing a nonlinearly implicit velocity-pressure solve?

> 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. 

I wouldn't put too much weight on "scaling with mesh size" per se. You want an efficient solver for the coarsest mesh that delivers sufficient accuracy in your flow regime. Constants matter.

Refining the mesh while holding time steps constant changes the advective CFL number as well as cell Peclet/cell Reynolds numbers. A meaningful scaling study is to increase Reynolds number (e.g., by growing the domain) while keeping mesh size matched in terms of plus units in the viscous sublayer and Kolmogorov length in the outer boundary layer. That turns out to not be a very automatic study to do, but it's what matters and you can spend a lot of time chasing ghosts with naive scaling studies.