[aspect-devel] Cylindrical coordinates

Jonathan Perry-Houts jperryh2 at uoregon.edu
Fri May 11 15:31:22 PDT 2018


The "repetitions" parameters can help with this, but refinements would
still be isotropic. Also, I've heard tell that the repetition parameters
aren't efficient for high-aspect-ratio meshes. My understanding is that
the MPI partitioning makes some assumptions based on how AMR "should" work.

Anyway, if someone figures out a workaround for mesh refinement, this
pseudo-2D hack could apply to the cylindrical case as well. Magali's
comment reminded me that Thorsten Becker and his group do this, too. I
guess it's common in Citcom, where 2D-3D is less trivial.

Is there an inherent performance hit when solving in 3D with Aspect
(beyond the ~doubling of DOF's)? I seem to remember that early on people
were noticing a substantial slow-down for similar size solutions, when
working in 3D.

On 05/11/2018 10:56 AM, Max Rudolph wrote:
> 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 <mailto: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>
>             <mailto: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>
>             <mailto:bangerth at colostate.edu <mailto:bangerth at colostate.edu>>
>                                       www:
>             http://www.math.colostate.edu/~bangerth/
>             <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
>         <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/
>         <http://www.tomforth.co.uk/genderbias/>
>         ___________________________________________________________
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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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> 
> 
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