[aspect-devel] On the van Keken benchmark

[Wolfgang Bangerth]

All:
following Cedric Thieulot's detective work, Timo Heister's preliminary 
computations, my suggestion, and Juliane Dannberg's follow-up, I think we have 
at least some kind of solution to the van Keken mystery.


Essentially, choosing a slightly smoothed out initial condition makes the 
benchmark converge nicely, and also match the results of van Keken. My 
write-up of what we've found here is in section 6.3.1 (page 91) of the manual at
   http://aspect.dealii.org/doc/manual.pdf
I would appreciate if people can give it a read (and suggest corrections and 
improvements).

To me, this essentially amounts to a flaw in the benchmark itself. What we 
have here is a case where small changes to the initial conditions (on the 
order of the mesh size) lead to results that are not just slightly different 
but in fact very different (the secondary plume rises at a completely 
different location). My view is that this is a poorly designed benchmark 
(certainly inadvertently so) not inherently a problem in Aspect. That said, we 
write Aspect for the community, and so what constitutes a problem is not 
something for me to judge but instead must be something that the community 
decides, and so I'd like everyone interested in the issue to please feel free 
to speak their mind.


Cedric: You've done all of these comparisons. The data I show in section 6.3.1 
currently use a fixed width for the smoothing of the initial conditions (the 
divisor 0.02 in the arc tangent) but a better choice would probably be to use 
a width that decreases as the mesh becomes finer. I think the value 0.02 is 
appropriate for 6 or 7 mesh refinements and should probably be reduced by a 
factor of 2 with every further mesh refinement. Are you interested in running 
a few more comparisons for quantitative comparisons as you've done for your 
AGU slides?


Best & thanks for everyone's help in figuring out what is happening here!
  Wolfgang
-- 
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Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/