[aspect-devel] On the van Keken benchmark

[Timo Heister]

Dear Cedric,

the drawbacks of smoothing is that it smears the interface, so it
potentially gives a less accurate solution. We do not need the
smoothing in this example because of "the advection scheme", but
because the setup of the problem makes it so that the position of the
second plume depends on the mesh otherwise.

That said, the right way would be:
- let the user specify if a given compositional field is a "yes"/"no" field
- treat those as a levelset that is initialized from a "yes"/"no"
initial condition (which produces a smooth function)
- implement correct treatment of the levelset (corrected advection
direction, reinitialization, maximum preserving time discretization?,
...)

I am not sure if there is anything that could be done easily in the
short term, though.


On Tue, Jan 14, 2014 at 12:45 PM, Thieulot, C. (Cedric)
<c.thieulot at uu.nl> wrote:
> Hi,
> just a quick word.
> I'll sure have a look at the van Keken once again with the arctan fix. I am happy to see that it seems to converge to a resolution-independent solution, congrats to the team.
> However, this begs the question:
> - 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 ?
>
> Cedric.
>
>
>
>
> On Jan 13, 2014, at 12:26 AM, Wolfgang Bangerth wrote:
>
>>
>> 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
>> --
>> ------------------------------------------------------------------------
>> Wolfgang Bangerth               email:            bangerth at math.tamu.edu
>>                                www: http://www.math.tamu.edu/~bangerth/
>>
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-- 
Timo Heister
http://www.math.clemson.edu/~heister/