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

[Wolfgang Bangerth]

Max,
first thanks for bringing these issues up, and documenting them well. I guess 
you have our attention, though I do like to point out that ASPECT has passed a 
fair number of benchmarks with results that match published data. I'm not 
trying to diminish your findings, but I'm also not yet convinced that every 
computation that has used ASPECT must be wrong :-)  (Or at least that's my 
hopeful optimism as one of the authors of the code...)


> So that it is documented on the mailing list, I wanted to summarize my 
> thoughts following the discussion this morning in the user meeting. The last 
> set of figures demonstrated that clearly the temperature stabilization is 
> causing too much diffusion and non-conservation of energy, even in problems 
> where the velocities are zero everywhere (zero peclet number) for which 
> stabilization is not necessary.

Here are a couple of things that would be interesting to figure out:
* If you output (graphically, via the viz postprocessor) the stabilization
   artificial viscosity, what do you find? The intent of the method used
   in ASPECT is that the artificial viscosity is (i) always at most as large
   as if one used a first-order articial viscosity method, and (ii) much
   smaller in all places where the residual is small -- i.e., where the
   temperature is smooth. I do recall that that was indeed the case for
   the original implementation, but the code as it is today is substantially
   different than the one I wrote for step-32 and that was used in early
   versions of ASPECT, and I would need to spend some time reading through it
   again.
* Do you actually see the same result if you used a Q1 element for the
   temperature equation? If you just look at the conduction problem, it
   shouldn't matter what element you use for the velocity/pressure (Q2/Q1
   vs Q1/P0), but ASPECT uses quadratic elements whereas most other codes
   use linear elements.
* It surprises me that "too much diffusion" should be the problem. That's
   because the depth-dependent temperature profile is already pretty much
   linear, and if there was too much diffusion, then it would be even more
   linear than the analytic solution. But your data shows that the temperature
   is *below* the convex analytic solution. I find it difficult to think
   in a sphere, so I may be completely wrong about this, but at least I
   haven't quite wrapped my head around this yet.

I guess you already have this on your list as well:
* Is this a problem with the spherical shell, or is it one that can be
   reproduced in a box geometry?


> I suggested that perhaps the SUPG approach used in venerable mantle convection 
> codes like CitcomS and ConMan could be superior because the artificial 
> diffusion acts along streamlines.

I think this would be interesting. I thought I recalled that Timo's student 
had implemented this in ASPECT, but one of his later emails suggests that that 
is not the case. It should not be terribly difficult to add, though.

I do recall discussions with the inventor of the entropy viscosity method 
about the fact that his method is isotropic whereas SUPG is not. His opinion 
was that it does not matter in practice, but I don't recall details.

Best
  W.


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