[petsc-users] Scalable Solver for Incompressible Flow

[Alexander Lindsay]

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.
>>>>>
>>>>
>>
>>
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