[petsc-users] Solving Stokes problem in high aspect ratio domains

[Hardik Kothari]

Dear Pierre, Dear PETSc team,

Thank you for your response.

In terms of geometry, we are moving toward more complex domains with more refined meshes that include multiple thin channels. We have been experimenting with the Stokes problem as a simplified case, but our main goal is to solve the high-Reynolds-number Navier–Stokes equations in these settings.

We are currently planning to utilize a multi-node CPU architecture.

For the Navier–Stokes system, we have experimented with both pressure-convection diffusion (PCD) and LSC preconditioners. In the thin channels, the PDC struggles to converge, and the LSC preconditioner is computationally slow, but it does converge eventually. Also, for both of these preconditioners for the thin channels, the norm of the preconditioned residual is much higher than the true residual norm, which likely indicates that neither preconditioner provides a sufficiently accurate approximation of the Schur complement.

I would appreciate any insights you may have for better preconditioning strategies.

Best regards,
Hardik



HARDIK KOTHARI

hardik.kothari at corintis.com<mailto:hardik.kothari at corintis.com>

Corintis SA
EPFL Innovation Park Building C
1015 Lausanne



[https://urldefense.us/v3/__https://storcor.s3.eu-central-1.amazonaws.com/logos/Logo-black.png__;!!G_uCfscf7eWS!ZkgL3p_ykjNhChJT714e-SsEGf_se8P03ZonnBbsSYm4XLTWR5khwNuHfc88CuP0c57UyPwjOWYcyMKkTLcXKGkCewbGGmUO$ ]
Here at Corintis we care for your privacy. That is why we have taken appropriate measures to ensure that the data you have provided to us is always secure
From: Pierre Jolivet <pierre at joliv.et>
Date: Sunday, 11 May 2025 at 20:45
To: Hardik Kothari <hardik.kothari at corintis.com>
Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Solving Stokes problem in high aspect ratio domains

You don't often get email from pierre at joliv.et. Learn why this is important<https://urldefense.us/v3/__https://aka.ms/LearnAboutSenderIdentification__;!!G_uCfscf7eWS!ZkgL3p_ykjNhChJT714e-SsEGf_se8P03ZonnBbsSYm4XLTWR5khwNuHfc88CuP0c57UyPwjOWYcyMKkTLcXKGkCe1E-JiqZ$ >

Do you want to refine the geometry or are you fine with the current one?
What kind of hardware are you planning on using (GPU, single-node…)?
Do you have a configuration for which LSC fails or does not give you good-enough performance?

Thanks,
Pierre


On 9 May 2025, at 9:08 PM, Mark Adams <mfadams at lbl.gov> wrote:

Hi Hardik,

The domain shape is not critical but the element shapes are. Your 100:1 domain aspect ratio is bad if you have N^3 mesh and thus element aspect ratios of 100:1.
If that is the case then you probably want to look at semi-coarsening multigrid.

Mark

On Fri, May 9, 2025 at 9:55 AM Hardik Kothari <hardik.kothari at corintis.com<mailto:hardik.kothari at corintis.com>> wrote:
Dear PETSc team,

We are solving the Stokes equations using PETSc (via Firedrake) on a highly anisotropic 3D domain (L_x=1, L_y=0.01, L_z=0.1).

In this setup, standard Schur complement preconditioners using a mass inverse for pressure struggle to converge. We could solve the problem with the LSC preconditioner (solver parameters are shown in the script).

We have the following questions:

 *   Why standard preconditioners struggle in such domains?
 *   Why is the preconditioned residual norm for the Schur complement system much higher than the true residual norm?
 *   Would you recommend alternative or more robust preconditioners for such geometries?

Thank you for your help.

Best regards,
Hardik



HARDIK KOTHARI

hardik.kothari at corintis.com<mailto:hardik.kothari at corintis.com>

Corintis SA
EPFL Innovation Park Building C
1015 Lausanne




[cid:~WRD0000.jpg]

Here at Corintis we care for your privacy. That is why we have taken appropriate measures to ensure that the data you have provided to us is always secure


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20250513/c6be9af0/attachment-0001.html>