[petsc-users] Scalable Solver for Incompressible Flow

Mon Jul 31 15:25:30 CDT 2023

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/
>
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