[aspect-devel] Cylindrical coordinates

[Jonathan Perry-Houts]

Maybe this could be the first 3.0 "milestone"!

Alternatively, someone could put together a geometry like 'chunk' that 
takes full spherical annulus, with some user-defined opening angle. That 
would probably be a lot easier.

On 05/11/2018 04:34 AM, 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!)
> 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 
>> <mailto: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 
>> <mailto:bangerth at colostate.edu>
>>                           www: http://www.math.colostate.edu/~bangerth/
>>
>> _______________________________________________
>> Aspect-devel mailing list
>> Aspect-devel at geodynamics.org <mailto:Aspect-devel at geodynamics.org>
>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/aspect-devel
> 
> ____________________________________________________________
> Professor of Geophysics
> Earth & Planetary Sciences Dept., UC Davis
> Davis, CA 95616
> 2129 Earth & Physical Sciences Bldg.
> Office Phone: (530) 752-4169
> http://magalibillen.faculty.ucdavis.edu
> 
> Currently on Sabbatical at Munich University (LMU)
> Department of Geophysics (PST + 9 hr)
> 
> Avoid implicit bias - check before you submit:
> http://www.tomforth.co.uk/genderbias/
> ___________________________________________________________
> 
> 
> 
> _______________________________________________
> Aspect-devel mailing list
> Aspect-devel at geodynamics.org
> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/aspect-devel
> 

-- 
Jonathan Perry-Houts
Ph.D. Candidate
Department of Earth Sciences
1272 University of Oregon
Eugene, OR 97403-1272