How to simulate Stokes/Creeping flow

[mhelel]

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Question

I want to simulate a Stokes/Creeping flow with MOOSE:

$$ \nabla u = 0 $$ $$ \eta\nabla^2 u = \nabla P $$

Since this problem is ill conditioned it doesn't scale good for large systems. I guess this problem was already solved in Moose but I wasn't able to find an example. I'm quite new to MOOSE so I just wanted to ask you, what would you reckon to be the best way to solve this system.

Additional information

No response

[lindsayad]

I would look at https://github.com/idaholab/moose/blob/next/modules/navier_stokes/test/tests/finite_element/ins/lid_driven/steady_vector_fsp_stokes.i which uses a Schur complement field split preconditioner. Since you are solving Stokes, the pressure mass matrix is spectrally equivalent to the Schur complement so you can use that as the preconditioner for the pressure split, which is what is done in that input