[CIG-CS] Discontinuous viscosity
walter at geodynamics.org
Mon Mar 5 07:01:20 PST 2012
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Matthew Knepley <knepley at mcs.anl.gov> wrote:
> 2012/3/4 Walter Landry <walter at geodynamics.org>
>> One interesting detail is that it is necessary to change the
>> fundamental variables, because I do not have expressions for the jumps
>> in velocity. To that end, I use the augmented velocity, which is the
>> ordinary velocity multiplied by the viscosity.
> 1) If you only use "augmented velocity" how do you write the continuity
With additional terms involving derivatives of the viscosity. When
writing Stokes this way, it turns out that it is very natural to use
the logarithm of the viscosity. I have not worked out the
implications of that, but at first blush it seems good.
> 2) You should be using PETSc, because even with GS, you could
> converge in 1000 iterations by partitioning fields using
> PCFIELDSPLIT. You could do it in < 10 using a nice Schur
> complement preconditioner.
Not yet. The point of this exercise is to have a method that I can
eventually plug into Gamr. Gamr uses SAMRAI, so I would only be able
to use Petsc for the solve on the coarsest level. I still need a
smoother for the finer levels.
> 3) I am more interested in unstructured for this case, but this will
> be good to compare with a Pylith-like scheme. I do not understand
> everything here. So it looks like viscosity is prescribed as an
> external function, right?
Exactly. Right now, the problem has constant, but discontinuous
viscosity. Eventually, I will also have to fix the derivatives in the
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