[petsc-users] Field Split PC for Fully-Coupled 3d stationary incompressible Navier-Stokes Solution Algorithm

[Dave May]

On 2 February 2015 at 10:39, Fabian Gabel <gabel.fabian at gmail.com> wrote:

> Dear PETSc Team,
>
> I implemented a fully-coupled solution algorithm (finite volume method)
> for the 3d stationary incompressible Navier-Stokes equations. Currently
> I am solving the resulting linear systems using GMRES and ILU and I
> wanted to ask, if solver convergence could be improved using a field
> split preconditioner.


Given the convergence in the attached file,
I would say yes, fieldsplit should be better.


> The possibility to use PCFIELDSPLIT (Matrix is
> stored as interlaced) has already been implemented in my solver program,
> but I am not sure on how to choose the parameters.
>

What do you mean? Is your matrix defined to have a block size of 4, or have
you set the IS's for each split (u,v,w,p)? The options for fieldsplit will
be different depending on the answer.

Before discussion any options for fielldsplit, what is App?
Is that an approximate pressure Schur complement?

Cheers,
  Dave


> Each field corresponds to one of the variables (u,v,w,p). Considering
> the corresponding blocks A_.., the non-interlaced matrix would read as
>
> [A_uu   0     0   A_up]
> [0    A_vv    0   A_vp]
> [0      0   A_ww  A_up]
> [A_pu A_pv  A_pw  A_pp]
>
> where furthermore A_uu = A_vv = A_ww. This might be considered to
> further improve the efficiency of the solve.
>
> You find attached the solver output for an analytical test case with 2e6
> cells each having 4 degrees of freedom. I used the command-line options:
>
> -log_summary
> -coupledsolve_ksp_view
> -coupledsolve_ksp_monitor
> -coupledsolve_ksp_gmres_restart 100
> -coupledsolve_pc_factor_levels 1
> -coupledsolve_ksp_gmres_modifiedgramschmidt
>
> Regards,
> Fabian Gabel
>
>
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