[CIG-CS] Discontinuous viscosity
Walter Landry
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
> equation?
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
viscosity.
Cheers,
Walter Landry
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