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

[Wolfgang Bangerth]

On 08/29/2018 01:16 PM, Rene Gassmoeller wrote:
> Hi all,
> 
> I think by now we have a pretty good understanding of the problem, 
> however there is no clear path forward yet. I have done some further 
> testing with the shell_simple_3d cookbook:
> 
>   - As Max pointed out the artificial viscosity at resolution <= 2 
> global refinement in spherical models is bigger than the natural 
> diffusion, although it reduces drastically with resolution (compare to a 
> natural conductivity of ~4 W/m*K).
> 
> Global refinement / Maximum artificial viscosity timestep 0 / timestep 2:
> 
> 1 (4 radial elements): 94.1 W/m*K  /  59.9 W/m*K
> 
> 2 (8 radial elements): 48.9 W/m*K / 6.12 W/m*K
> 
> 3 (16 radial elements): 24.8 W/m*K / 0.92 W/m*K

It's worth pointing out that the time step size in time step zero is 
zero, so even though the artificial viscosity is large, no diffusion is 
actually happening because the time step size is zero.

The important quantity is indeed the second column -- it's interesting 
to see that it is proportional to h^2.

> 1. Allow for different stabilization parameters for temperature and 
> composition, and check which values are still stable.

You could just take the maximum of physical and artificial diffusion 
parameters, instead of the sum. Since the parameters are tuned for 
problems with no physical diffusion, this should work.


> 2. Do not stabilize advection/diffusion solutions where the velocity is 
> zero (because it is only a diffusion equation).

You will want to make sure that there is *some* diffusion in this case. 
If the velocity is zero but the physical diffusion is also zero, you 
will probably need *some* kind of artificial diffusion. That's because 
if you don't, then you basically just have an ODE at every point of the 
domain, and your solution will not retain any kind of spatial correlation.

Best
  W.

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