[petsc-users] Scalable Solver for Incompressible Flow

[Alexander Lindsay]

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