[aspect-devel] questions regarding accuracy of no-heat flux boundary condition and help needed for the right entropy viscosity parameters

[Ying He]

Dear all,

I was running several tests on Stratified Density ('Buoyancy') problem 
with comparison between FEM and DG methods. The FEM prm file is 
attached.

The no heat flux boundary conditions are assigned at left and right 
walls of a rectangular box. My first question is that the no heat flux 
boundary condition seems not preserved for both FEM and DG methods after 
long time computation, see attached pdf "T_no_hear_flux_plot.pdf". I 
thought it perhaps dues to that we don't have enough resolution points 
near the 'non-flat but sharp' boundary values near the left and right 
walls, see the cross lines on "T_cross2.png"; but I also want to make 
sure it is not a side effect of the extra entropy viscosity 
stabilization from the FEM approach or the "penalty terms" from the DG 
approach. Hope anyone can clarify this for me.

As shown in the figure 'timeE10.png', the final solutions of FEM(right) 
and DG(left) are very different. The fem results are more diffusive than 
the DG results. The prm file of FEM approach is attached. Since the test 
example uses constant viscosity, the harmonic average will not help 
here. Also the numerical results doesn't show much overshoot/undershot, 
so I guess modifying the "alpha" value is also not helpful. Does anyone 
know that there has other parameters regarding entropy viscosity I 
should try?

An annimation of the comparison in time can be checked at here
https://www.math.ucdavis.edu/~yinghe/tmp/animated2.gif

-- 
Best,
Ying He
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