[petsc-users] Fwd: SNES examples question

[Jed Brown]

On Sat, May 14, 2011 at 02:53, Barry Smith <bsmith at mcs.anl.gov> wrote:

> Do you know what the valid values for the various model parameters in snes
> ex20 and ex29 are? We are looking for something we can vary similar to how
> we change the lid velocity and grashof parameters in the driven cavity
> problems, in order to generate linear systems with different
> characteristics.


The options are given in the help strings. Do you want the names of the
non-dimensional parameters? Do you want to know how various parameters
affect the system?

In the case of ex20, the exponent beta is the only free parameter. If
temperature is always positive, I believe there are no well-posedness issues
for any beta. Positive beta becomes degenerate as T -> 0, negative beta
becomes singular in that limit. It appears that the method works for all
positive beta. When beta is negative, this discretization (or maybe just the
line search) is not monotone so it may compute negative temperatures
(program crashes). Negative beta is physical for other heat transport
problems.

I can't give a similarly detailed explanation of ex29, but low viscosity and
low resistivity should tend to make it less diffusive (closer to ideal MHD
which is hyperbolic). This discretization seems to produce singular linear
systems.
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