[aspect-devel] Cylindrical coordinates

[Wolfgang Bangerth]

On 05/11/2018 07:34 PM, Magali Billen wrote:
> 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!)

That is a fair point. It originates in the deal.II habit of doing things in a 
dimension-independent way and thus the need to have a name for this kind of 
geometry that is independent of the dimension. We have typically chosen these 
names as derived from the 3d case: hyper-cube, hyper-sphere, hyper-shell, etc.

That said, I agree that this naming is misunderstandable and will add some 
text to the documentation of these models tomorrow.


> 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.

Well, I think one can probably see this in many different ways. But it is true 
that when we say "2d", we think of this in Cartesian coordinates and 
consequently as you already point out (suggestions for improvements of the 
text welcome!):


> 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.

I'd like to point out that indeed that is what many papers use as well for 
their definition of 2d. Think of all of the 2d benchmarks, for example, which 
are almost all defined in exactly this kind of way.

Now, it is true that one can conveniently write many models in r-z and 
interpret that then as a cross section of a body of rotation. This is not a 
frequently requested feature (I'm sure this has come up a couple of times over 
the ~8 years of ASPECT, but not much more often), and so it is not 
implemented. It is simply a question of who takes the time to implement it and 
find all of the places where one needs to change things..

Best
  W.

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