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

[Wolfgang Bangerth]

> Thank you for summarizing the current state of affairs. I would suggest 
> that when you make the changes in (1)-(2), you also make ASPECT print at 
> least a warning when the entropy viscosity exceeds, say, 1% of the 
> thermal conductivity. It might be even better for the code to exit in 
> with an error unless a parameter is explicitly set to ignore such a 
> condition.

Nah, that can't work :-)

If your Rayleigh number is large (i.e., the physical diffusion constant 
is small), then the artificial diffusion will always be larger by a 
significant fraction than the physical one unless you have an 
exceedingly fine mesh capable of resolving the boundary layer width. But 
in practice, you will not likely be able to do that, and in that case 
the artificial diffusion must be larger than the physical one.

You are thinking of cases where the Peclet number is zero because the 
velocity is zero. In that case, the boundary layer width is infinite and 
any mesh is fine enough to resolve it. But that's a very specific case.


> It also seems that one way around (1) is to use DG elements for 
> composition. Is this what most users are doing anyways?

I don't know, but it's worth noting that DG methods are not magic bullet 
either as they also have diffusion.

The amount of diffusion you get is controlled by the stabilization 
constant in the DG formulation. That value is chosen in a way to make 
the method stable, but it is nonzero and so you do have diffusion there 
as well. I can imagine that the *amount* of diffusion you get that way 
is smaller by a certain factor, but my intuition tells me that it will 
not be *qualitatively* different from what you get with a stabilized CG 
method.

Best
  W.

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