[petsc-users] Preconditioner for stokes flow with mixed boundary conditions.

Matthew Knepley knepley at gmail.com
Mon Apr 19 05:31:26 CDT 2021

On Mon, Apr 19, 2021 at 6:18 AM Abhinav Singh <abhinavrajendra at gmail.com>

> Hello all,
> I am trying to solve for incompressible stokes flow on a particle based
> discretization. I use a pressure correction technique along with Particle
> strength exchange like operators.
> I call Petsc to solve the Stokes Equation without the pressure term.

What does this mean? Stokes means using an incompressibility constraint,
for which we often introduce a pressure.

Do you mean you are solving only the momentum block? If so, do you have a
constant viscosity? If so, then this is just the Laplace equation.
You should use a good Laplacian preconditioner, like -pc_type gamg or
-pc_type ml.



> GMRES usually works great but with dirichlet boundary conditions. When I
> use a mixed boundary condition in Y, (dirichlet on bottom and Neumann on
> the top) with periodicity in X,Z. GMRES fails converge when the size of
> matrix increases. For smaller size (upto 27*27*5), only GMRES works and
> that too only with the option 'pc_type none'. I was unable to find any
> preconditioner which worked. Eventually, it also fails for bigger size.
> UMFPACK works but LU decomposition fails after a certain size and is very
> slow.
> It would be great if you could suggest a way or a preconditioner which
> suits this problem.
> Kind regards,
> Abhinav

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/>
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