[aspect-devel] Cylindrical coordinates

Fri May 11 10:56:19 PDT 2018

The problem with approaching the spherical annulus as a small-opening angle
chunk is that deal.ii does not support anisotropic refinement. So, if you
need to refine in the depth or longitude directions, you will also end up
adding unnecessary degrees of freedom in the latitude direction as well.
That said, this could probably be implemented very quickly whereas changing
the governing equations to reflect spherical geometry with the assumption
of d/dtheta (theta is colat) would possibly be a lot harder and would
probably necessitate changes in many other parts of the code.

On Fri, May 11, 2018 at 10:02 AM, Jonathan Perry-Houts <jperryh2 at uoregon.edu
> wrote:

> 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/
>>>
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>>
>> ____________________________________________________________
>> 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:
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>> ___________________________________________________________
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>>
> --
> Jonathan Perry-Houts
> Ph.D. Candidate
> Department of Earth Sciences
> 1272 University of Oregon
> Eugene, OR 97403-1272
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