[petsc-users] Scalable Solver for Incompressible Flow

Mon Jul 31 17:09:56 CDT 2023

I would email the author. He's been helpful in the past and that newer paper may have been extensions that didn't make it into the upstream example.

Alexander Lindsay <alexlindsay239 at gmail.com> writes:

> Maybe that example was a jumping point for some of those studies, but it
> looks to me like that example has been around since ~2012 and initially
> only touched on SIMPLE, as opposed to addition of SIMPLE into an
> augmented lagrange scheme.
>
> But it does seem that at some point Carola Kruse added Golub-Kahan
> bidiagonalization tests to ex70. I don't know very much about that although
> it seems to be related to AL methods ... but requires that the matrix be
> symmetric?
>
> On Fri, Jul 28, 2023 at 7:04 PM Jed Brown <jed at jedbrown.org> wrote:
>
>> See src/snes/tutorials/ex70.c for the code that I think was used for that
>> paper.
>>
>> Alexander Lindsay <alexlindsay239 at gmail.com> writes:
>>
>> > Sorry for the spam. Looks like these authors have published multiple
>> papers on the subject
>> >
>> > cover.jpg
>> > Combining the Augmented Lagrangian Preconditioner with the Simple Schur
>> Complement Approximation | SIAM Journal on
>> > Scientific Computingdoi.org
>> > cover.jpg
>> >
>> >  On Jul 28, 2023, at 12:59 PM, Alexander Lindsay <
>> alexlindsay239 at gmail.com> wrote:
>> >
>> >  Do you know of anyone who has applied the augmented Lagrange
>> methodology to a finite volume discretization?
>> >
>> >  On Jul 6, 2023, at 6:25 PM, Matthew Knepley <knepley at gmail.com> wrote:
>> >
>> >  On Thu, Jul 6, 2023 at 8:30 PM Alexander Lindsay <
>> alexlindsay239 at gmail.com> wrote:
>> >
>> >  This is an interesting article that compares a multi-level ILU
>> algorithm to approximate commutator and augmented
>> >  Lagrange methods: https://doi.org/10.1002/fld.5039
>> >
>> >  That is for incompressible NS. The results are not better than
>> https://arxiv.org/abs/1810.03315, and that PC is considerably
>> >  simpler and already implemented in PETSc. There is an update in to this
>> >
>> >
>> >
>> https://epubs.siam.org/doi/abs/10.1137/21M1430698?casa_token=Fp_XhuZStZ0AAAAA:YDhnkW9XvAom_b8KocWz-hBEI7FAt46aw3ICa0FvCrOVCtYr9bwvtqJ4aBOTkDSvANKh6YTQEw
>> >
>> >
>> >  which removes the need for complicated elements.
>> >
>> >  You might need stuff like ILU for compressible flow, but I think
>> incompressible is solved.
>> >
>> >    Thanks,
>> >
>> >       Matt
>> >
>> >  On Wed, Jun 28, 2023 at 11:37 AM Alexander Lindsay <
>> alexlindsay239 at gmail.com> wrote:
>> >
>> >  I do believe that based off the results in
>> https://doi.org/10.1137/040608817 we should be able to make LSC, with
>> >  proper scaling, compare very favorably with PCD
>> >
>> >  On Tue, Jun 27, 2023 at 10:41 AM Alexander Lindsay <
>> alexlindsay239 at gmail.com> wrote:
>> >
>> >  I've opened https://gitlab.com/petsc/petsc/-/merge_requests/6642 which
>> adds a couple more scaling
>> >  applications of the inverse of the diagonal of A
>> >
>> >  On Mon, Jun 26, 2023 at 6:06 PM Alexander Lindsay <
>> alexlindsay239 at gmail.com> wrote:
>> >
>> >  I guess that similar to the discussions about selfp, the approximation
>> of the velocity mass matrix by the
>> >  diagonal of the velocity sub-matrix will improve when running a
>> transient as opposed to a steady
>> >  calculation, especially if the time derivative is lumped.... Just
>> thinking while typing
>> >
>> >  On Mon, Jun 26, 2023 at 6:03 PM Alexander Lindsay <
>> alexlindsay239 at gmail.com> wrote:
>> >
>> >  Returning to Sebastian's question about the correctness of the current
>> LSC implementation: in the
>> >  taxonomy paper that Jed linked to (which talks about SIMPLE, PCD, and
>> LSC), equation 21 shows four
>> >  applications of the inverse of the velocity mass matrix. In the PETSc
>> implementation there are at
>> >  most two applications of the reciprocal of the diagonal of A (an
>> approximation to the velocity mass
>> >  matrix without more plumbing, as already pointed out). It seems like
>> for code implementations in
>> >  which there are possible scaling differences between the velocity and
>> pressure equations, that this
>> >  difference in the number of inverse applications could be significant?
>> I know Jed said that these
>> >  scalings wouldn't really matter if you have a uniform grid, but I'm not
>> 100% convinced yet.
>> >
>> >  I might try fiddling around with adding two more reciprocal
>> applications.
>> >
>> >  On Fri, Jun 23, 2023 at 1:09 PM Pierre Jolivet <pierre.jolivet at lip6.fr>
>> wrote:
>> >
>> >  On 23 Jun 2023, at 10:06 PM, Pierre Jolivet <pierre.jolivet at lip6.fr>
>> wrote:
>> >
>> >  On 23 Jun 2023, at 9:39 PM, Alexander Lindsay <alexlindsay239 at gmail.com>
>> wrote:
>> >
>> >  Ah, I see that if I use Pierre's new 'full' option for
>> -mat_schur_complement_ainv_type
>> >
>> >  That was not initially done by me
>> >
>> >  Oops, sorry for the noise, looks like it was done by me indeed in
>> >  9399e4fd88c6621aad8fe9558ce84df37bd6fada…
>> >
>> >  Thanks,
>> >  Pierre
>> >
>> >  (though I recently tweaked MatSchurComplementComputeExplicitOperator()
>> a bit to use
>> >  KSPMatSolve(), so that if you have a small Schur complement — which is
>> not really the case
>> >  for NS — this could be a viable option, it was previously painfully
>> slow).
>> >
>> >  Thanks,
>> >  Pierre
>> >
>> >  that I get a single iteration for the Schur complement solve with LU.
>> That's a nice testing
>> >  option
>> >
>> >  On Fri, Jun 23, 2023 at 12:02 PM Alexander Lindsay <
>> alexlindsay239 at gmail.com>
>> >  wrote:
>> >
>> >  I guess it is because the inverse of the diagonal form of A00 becomes a
>> poor
>> >  representation of the inverse of A00? I guess naively I would have
>> thought that the
>> >  blockdiag form of A00 is A00
>> >
>> >  On Fri, Jun 23, 2023 at 10:18 AM Alexander Lindsay <
>> alexlindsay239 at gmail.com>
>> >  wrote:
>> >
>> >  Hi Jed, I will come back with answers to all of your questions at some
>> point. I
>> >  mostly just deal with MOOSE users who come to me and tell me their
>> solve is
>> >  converging slowly, asking me how to fix it. So I generally assume they
>> have
>> >  built an appropriate mesh and problem size for the problem they want to
>> solve
>> >  and added appropriate turbulence modeling (although my general
>> assumption
>> >  is often violated).
>> >
>> >  > And to confirm, are you doing a nonlinearly implicit
>> velocity-pressure solve?
>> >
>> >  Yes, this is our default.
>> >
>> >  A general question: it seems that it is well known that the quality of
>> selfp
>> >  degrades with increasing advection. Why is that?
>> >
>> >  On Wed, Jun 7, 2023 at 8:01 PM Jed Brown <jed at jedbrown.org> wrote:
>> >
>> >  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.
>> >
>> >  --
>> >  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/
>>