[aspect-devel] Internal heating in aspect (Ludovic Jeanniot)

[Wolfgang Bangerth]

On 08/29/2018 07:15 AM, Juliane Dannberg wrote:
> I think the reason for the lower artificial diffusion closer to the 
> core-mantle boundary is just the different cell size. The stabilization 
> scales with the actual cell size, so it is smaller for smaller cells.

Yes, that is correct.


> But I agree that this becomes a substantial problem as soon as the 
> artificial diffusion approaches (or even exceeds) the physical 
> diffusion, as in Max' example. This also made me wonder if this is one 
> of the reasons why the problem is more apparent in spherical models. In 
> a box model, the diffusion that's added is similar at the top and bottom 
> (at least for a uniform grid), while in the spherical case, it's much 
> bigger the closer you get to the surface, which leads to a big asymmetry 
> of the heat flux, and a change in temperature.

The issue is that (at least for models where the velocity is not zero) 
you need to bring the cell Peclet number below one. If the velocity is 
roughly constant throughout the domain, then the Peclet number scales 
with the mesh size, and that implies that you have to choose an 
artificial viscosity (artificial conductivity) that also scales with the 
mesh size.

That's clearly a nuisance in the current case, but there is little you 
can do about it, and it's the same for all stabilization schemes you 
could come up with.

Cheers
  W.

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