[aspect-devel] Onset of convection, time step choice

[Max Rudolph]

Dear All,
I am teaching geodynamic modeling this term, and asked my students as an
introductory assignment to try to use ASPECT to determine experimentally
the critical Rayleigh number for the onset of convection for an isoviscous
fluid, heated from below with free-slip boundary conditions. The students
did this by modifying cookbooks/convection-box.prm. One student found that
convection began at Ra less then half the critical Ra for the chosen aspect
ratio of 4:3. Of course, it turned out that too large a timestep was
allowed. If the timestep size is limited to, say 100 Myr, we recover the
correct value of Ra_{cr} within ~5% even for relatively coarse meshes
(refinement level 4). I was a bit surprised, however, that the default
timestep taken by ASPECT was so large. In fact, we had convergence problems
for higher refinement levels for the default maximum timestep. For a
problem like the one that we were running, a reasonable maximum timestep
seems to be L^2/kappa (thermal diffusion timescale), where L is a
characteristic length scale for the domain. Does it seem reasonable to
change the way that ASPECT computes the maximum time step based on this
idea rather than using 10^300 (the current default value, which seems
entirely arbitrary)? I am happy to submit a pull request to do this, but
don't want to waste my time if it's unlikely to be accepted.

Cheers
Max
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