[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
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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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