[aspect-devel] Cylindrical coordinates

[Magali Billen]

It is really too bad that the 2D version of something called “spherical shell” ends up being implemented as an infinite cylinder (how very strange!)
For one, it derives from thinking in Cartesian space, and not as an “earth” scientist (we live on a sphere).  And, it really detracts from 
what is advertised as the ease in switching from 2D (eg., for testing) to 3D in Aspect. In reality, it seems, this only works in cartesian coordinates.

This also should be made much more explicit (like use the words “infinite cylinder” in the manual), because it is really not obvious
from the description in the manual, which is explained in cartesian coordinates (I doubt the implication in spherical coordinates is obvious to most
readers - it certainly wasn’t to me):

The notion we adopt here – in agreement with that chosen by many other codes – is to think of two- dimensional models in the following way: We assume that the domain we want to solve on is a two-dimensional cross section (parameterized by x and y coordinates) that extends infinitely far in both negative and positive z direction. Further, we assume that the velocity is zero in z direction and that all variables have no variation in z direction. As a consequence, we ought to really think of these two-dimensional models as three-dimensional ones in which the z component of the velocity is zero and so are all z derivatives. 

The one way that one could go from smaller 2D models in actual spherical geometry would be to use the Chunk geometry with one cell in the
latitude direction, but you can’t do a full annulus.  This is essentially what I’ve been using for regional 2D models in CitcomS. I had been looking forward
to easily stepping from 2D spherical slices (regional using Chunk) to 2D spherical annulus  to test the effects of side-walls (then to 3D), but now I realize 
that also have to contend with the possible effects of a cylindrical geometry assumption.  Bummer :-(   

> On May 11, 2018, at 9:21 AM, Wolfgang Bangerth <bangerth at colostate.edu> wrote:
> 
> 
>> Cylindrical coordinates has been on my radar for a while, but I'm
>> probably not going to pursue it right now. I'm trying to wrap up this
>> whole dissertation thing, and need to weigh the time commitment of
>> adding this feature vs. time to just run the models in 3D. Seems like 3D
>> Cartesian wins again. As always, XKCD sums up my predicament well:
>> https://xkcd.com/974/
> 
> :-)
> 
> 
>>> My understanding is that in 2D, the spherical shell model is equivalent
>>> to a 2D annulus.
> 
> Correct. It corresponds to a horizontal slice through an infinity cylinder whose central region you have excluded (i.e., a cross section through the metal part of a pipe).
> 
> 
>>> I was suggesting the spherical annulus, which is actually a three
>>> dimensional equatorial slice with a very small latitudinal opening
>>> angle. This is like taking a (thin) slice of pizza, tipping it sideways,
>>> and making a volume of revolution :). In this geometry the area ratios
>>> of the surface and CMB are preserved.
> 
> So you expect a latitudinal variation but not a variation in angular direction and consequently want to simulate in the r/theta plane but ignore phi? Or do I misunderstand and you really want to simulate in the r/theta plane and say that the variation in phi is so small that there is no variation?
> 
> Best
> W.
> 
> 
> -- 
> ------------------------------------------------------------------------
> Wolfgang Bangerth          email:                 bangerth at colostate.edu
>                           www: http://www.math.colostate.edu/~bangerth/
> 
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____________________________________________________________
Professor of Geophysics 
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Currently on Sabbatical at Munich University (LMU)
Department of Geophysics (PST + 9 hr)

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