[aspect-devel] Cylindrical coordinates

[Wolfgang Bangerth]

On 05/12/2018 01:56 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.

Yes, this is all correct. (Though one could nit-pick that deal.II *does* 
support anisotropic refinement -- just not for parallel computations.)

Of course, even if you could restrict things to one cell in latitude 
direction, you would still have the possibility of variation in this 
direction. This could be addressed in one central place by enforcing that the 
field does not vary in this direction via constraints (which could also take 
care of the case that you have multiple cells in latitude), though this is of 
course no efficient since the linear systems are larger than necessary.

Best
  W.

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