[petsc-users] Pre-conditioner for parallel CFD simulation

[Jed Brown]

On Thu, Apr 14, 2011 at 20:22, Denner, Fabian <f.denner09 at imperial.ac.uk>wrote:

> It's Finite Volume, co-located grid arrangement, stabilized, with a
> continuous pressure field at CFL numbers < 1 (typically 0.3-0.7).
>

Much easier, it is likely that a relatively standard coupled multigrid will
work. If you order unknowns so they are interlaced (u0,v0,w0,p0,u1,v1,...)
and MatSetBlockSize(A,4) and/or use the BAIJ format, you stand a good chance
with -pc_type ml and reasonable smoothers. Or you may have access to a
geometric hierarchy?

Preconditioning with SIMPLE, or (stronger) using SIMPLE as a smoother on
multigrid levels should work well. With the CFL number so low (and even
lower on coarse levels), you can also skip the SIMPLE procedure and just use
the "pressure Poisson" operator from the usual semi-implicit method as a
preconditioner (or as a smoother for coupled multigrid, with Jacobi applied
to the velocity part). Any of these variants should converge in a small
number of iterations independent of resolution.

The following does not do any coupled multigrid (which should converge
faster, but is more expensive per V-cycle), but should give you a good
methods intro. All these algorithms are straightforward to implement using
PCFieldSplit.

http://dx.doi.org/10.1016/S0021-9991(03)00121-9
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