[petsc-users] Scalable Solver for Incompressible Flow

[Alexander Lindsay]

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.
>>>>
>>>
>
>
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