Roger,
In that example, we scaled the pressure appropriately such that the
solution is stable with physical units for viscosity (~10^22 Pa s).
However, in my simulation, I would like to solve the Stokes equations
for a medium with a large (5 orders +) viscosity contrast. Using a
single pressure scaling as in step-32 is stable with viscosity
contrasts up to ~ 3 orders. I've tried a sharp viscosity contrast as
well as a continuous one where the viscosity contrast across each
cell is no more than a factor of a few. Still no reasonable
solution! By inspection, it looks like the ( div u = 0 ) condition
is not met in the solutions.
What is a way to deal with this? In the geophysics literature people
have solved problem in a couple of ways, but implementing those fixes
would mean almost starting from scratch for my code. Has anyone
dealt with large viscosity contrasts in deal.ii? If so, any help is
greatly appreciated!
This is something that we need to address eventually in the new ASPECT
code, see
http://dealii.org/aspect/
(the website is still in the process of being written). That said, I
don't think that we can say we have figured out the answer to your
question so far.
One thing I would definitely try out is how to scale the pressure. If
you feel like the divergence condition is not satisfied, then you may
want to make the pressure scaling larger or smaller; or tighten the
tolerances of the linear solvers. Apart from that, we'd certainly be
very interested in hearing what you find out!
Best
Wolfgang
------------------------------------------------------------------------
Wolfgang Bangerth email: [email protected]
www: http://www.math.tamu.edu/~bangerth/
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