[aspect-devel] On the van Keken benchmark

[Wolfgang Bangerth]

Hi Cedric,

> - in this particular case, the interface was easily smoothedbecause
> it was a simple sinusoidal function. What if the interface displayed
> sharp angles, or even right angles ? Prescribing a smoothed version
> of the interface would be extremely cumbersome from the input file
> with a parser. In light thereof, should there not be a 'smoothing
> function' in aspect which would automatically smooth any composition
> interface with to a certain width ?
 >
> - Should interfaces always be smoothed at startup ?  Given the
> advection scheme it sounds like a good idea.  What would be the
> drawbacks ?

You reduce the accuracy of the solution by smoothing. I don't think that 
we need to do it always -- I think what this just shows is that the 
benchmark is poorly designed. What the smoothing demonstrates is that a 
small change in the initial conditions leads to a large change in the 
response. You will, in general, not be able to get reliable results out 
of benchmarks like this unless you do tricks like the smoothing we used. 
I would not be surprised if some of the codes compared in the paper also 
resorted to playing with things until they got the "right" answer 
(however, I do not know this for sure, of course, not having talked to 
any of the people involved in the paper).

Of course, well designed benchmarks do not exhibit this kind of 
behavior: there, small changes in the initial conditions will only yield 
small changes in the observed behavior, and in those cases there will be 
no need to smooth out initial conditions etc. An example is the first 
peak, which got resolved perfectly with either the discontinuous or the 
smoothed initial condition. There, no smoothing or other trickery was 
necessary and, in fact, any of that would have been counter-productive.

Does this make sense?

Best
  Wolfgang

-- 
------------------------------------------------------------------------
Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/