# [CIG-CS] Discontinuous viscosity

Walter Landry walter at geodynamics.org
Mon Mar 5 07:01:20 PST 2012

```Back to the list.

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
```