You might want to have a look at the step-35 example that discusses a
projection-based approach for the Navier-Stokees equations.

Best,
Daniel

On Wed, Feb 19, 2025 at 1:36 PM Md Mahmudul Islam
<mahmudulislampri...@gmail.com> wrote:
>
> Hello Everyone,
> Hope you all are doing great. I did my time-dependent NSE flow problem 
> coupled scheme problem following step-22. Now I am having an issue with 
> penalty projection of the same problem. While I decoupled pressure to step 2, 
> I am getting errors for my local matrix 1 from step 1 which has only velocity 
> and viscosity. I think, I know the problem, which is as, I decoupled pressure 
> from step 1 to step 2, my local matrix 1 is becoming rank deficit. I am using 
> UMFPACK solver to solve my matrix. Is there any step or any source that can 
> help me to solve my problem?
>
> Thanks to everyone in this nice group.
>
> Best Regards,
> Md Mahmudul Islam
>
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