On Thu, Jul 6, 2023 at 8:30 PM Alexander Lindsay <[email protected]> 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 < > [email protected]> 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 < >> [email protected]> 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 < >>> [email protected]> 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 < >>>> [email protected]> 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 <[email protected]> >>>>> wrote: >>>>> >>>>>> >>>>>> On 23 Jun 2023, at 10:06 PM, Pierre Jolivet <[email protected]> >>>>>> wrote: >>>>>> >>>>>> >>>>>> On 23 Jun 2023, at 9:39 PM, Alexander Lindsay < >>>>>> [email protected]> 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 < >>>>>> [email protected]> 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 < >>>>>>> [email protected]> 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 <[email protected]> wrote: >>>>>>>> >>>>>>>>> Alexander Lindsay <[email protected]> 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/ <http://www.cse.buffalo.edu/~knepley/>
