[aspect-devel] Help needed with setting up an EBA benchmark

[Wolfgang Bangerth]

On 09/04/2014 08:10 PM, Katrina Arredondo wrote:
> Here at Davis the ASPECT discussion group has repeatedly asked ourselves what
> is the best way to translate the dimensional terms in ASPECT into the
> nondimensional Rayleigh and Dissipation numbers during postprocessing.

That is of course the question at the heart of the matter: if you don't know 
how to translate from physical quantities to nondimensional ones, then the 
other direction is equally ill-defined.

To give an example, the Rayleigh number is defined as
   Ra = alpha g dT L^3 / eta k
In realistic cases, every single one of these physical quantities is spatially 
variable as they depend on temperature, pressure and, in the case of gravity, 
on basically everything everywhere. For the temperature difference dT, one may 
ask where the upper and lower temperatures should be taken if you consider the 
Earth (top of the crust, bottom of the crust?) or a regional model. Finally, 
what exactly is the length scale L? If you have a regional model with a 
subducting slab, is L the horizontal extent of your domain? The vertical 
extent? Maybe the size of the convecting wedge above the subducting slab and 
the overriding plate?

What then *is* the Rayleigh number? Even if there was a good way to define dt 
and L, it would be different at every point of the domain, of course. What I 
mean to say by this is that dimensionless quantities are only defined in 
simple cases with constant coefficients -- the things we have known how to do 
for a long time in geodynamics and that we are now trying to move beyond. 
These were my considerations when I thought about how one describes cases in 
ASPECT when I was designing the code: would I stick with how it has been done 
in the past but that is no longer adequate when you want to use complex cases, 
or should I "break backward compatibility" and force everyone to describe 
things in physical quantities and, if they wanted to, let them compute 
nondimensional quantities as a postprocess using some appropriate "reference 
viscosity", "reference thermal expansion coefficient", etc. I continue to 
believe that the way we chose to do it was the right way forward.

Best
  Wolfgang

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