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

[Magali Billen]

Wolfgang, I completed agree - for the types of problems people are working on now, non-dimensional
calculations make no sense.

I've basically been using CitcomS "dimensionally", but with constant coefficients(alpha, k, g) since my post-doc.
I always design a dimensional problem, choose "reference" values and then calculate the effective Rayleigh number
and Dissipation number to input into the code. When I first starting doing this, I struggled with which value to use 
for the reference viscosity in the Rayleigh number, but then I just stop reporting a Rayleigh number (or dissipation number)
in my papers because they are meaningless, and I just reported the table of values and the equations defining how 
these parameters varied (viscosity, density).

Magali

On Sep 7, 2014, at 3:08 PM, Wolfgang Bangerth <bangerth at tamu.edu> wrote:

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