[petsc-users] Multigrid preconditioning of entire linear systems for discretized coupled multiphysics problems

[Jed Brown]

Fabian Gabel <gabel.fabian at gmail.com> writes:

> AMG has apparently been used (successfully?) for fully-coupled
> finite-volume discretizations of Navier-Stokes:
>
> http://dx.doi.org/10.1080/10407790.2014.894448
> http://dx.doi.org/10.1016/j.jcp.2008.08.027

These papers effectively bring a pressure projection or SIMPLE-type
algorithm into a coupled system.  It's not a saddle-point formulation
and is not uniformly valid across parameters (I think; methods of this
sort normally aren't, but I haven't analyzed it).  The multigrid
algorithm is not described and might not be purely algebraic.

Note that the 2014 paper copies liberally from the 2009 paper.

You can try formulating Navier-Stokes this way and test existing solvers
if you like, but I predict it doesn't come without tradeoffs.
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