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

Abhinav Singh abhinavrajendra at gmail.com
Mon Apr 19 13:37:51 CDT 2021

```Hello,

The Stokes flow equations are a 3d version of the equations attached
(Stokes-Leslie Flow). Only variables/unknowns are v and
u_xy=0.5(Dx(vy)+Dy(vx).

I am trying to solve them iteratively by correcting the pressure to reach a
first iteration (periodic in X and Z. V=0 at Y=0 and Dx(vy)+Dy(vx)=g(x) at
Y=10).

I think the equations might be singular but I am not sure as in my
experience, the problem is well posed if the solution is known at certain
boundaries.

[image: by default 2021-04-19 at 20.28.28.png]

On Mon, 19 Apr 2021 at 15:59, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Apr 19, 2021 at 9:37 AM Abhinav Singh <abhinavrajendra at gmail.com>
> wrote:
>
>> What does this mean? Stokes means using an incompressibility constraint,
>>> for which we often introduce a pressure.
>>
>> Yes, what I mean is solving the momentum block, say with known pressure.
>> viscosity is constant however, the momentum equation has both Laplacian and
>>
>
> That does not make any sense to me. Can you write the equation?
>
>   Thanks,
>
>      Matt
>
>
>> You should use a good Laplacian preconditioner, like -pc_type gamg or
>>> -pc_type ml.
>>
>> I tried gamg and it seems to diverge as the solution is NaN. The KSP
>> residual message is " 0 KSP Residual norm 1.131782747169e+01  ".
>> When using -pc_type ml, I get Aggregate Warning and then some faulty
>> address which stops the code.
>>
>>
>>
>> On Mon, 19 Apr 2021 at 12:31, Matthew Knepley <knepley at gmail.com> wrote:
>>
>>> On Mon, Apr 19, 2021 at 6:18 AM Abhinav Singh <abhinavrajendra at gmail.com>
>>> wrote:
>>>
>>>> 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.
>>>
>>>   Thanks
>>>
>>>      Matt
>>>
>>>
>>>> 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
>>> -- Norbert Wiener
>>>
>>> https://www.cse.buffalo.edu/~knepley/
>>> <http://www.cse.buffalo.edu/~knepley/>
>>>
>>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
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