[firedrake] Perturbed extruded meshes

[Lawrence Mitchell]

On 2 Mar 2015, at 12:12, Eike Mueller <e.mueller at bath.ac.uk> wrote:

> Dear all,
> 
> is there a 2d square mesh with periodic boundary conditions or is this only supported in 1d? I realised that to get steep orography in my setup I would either have to work at very high resolution or shrink the size of the earth.
> 
> So I thought instead it would be easier if I work in a 2+1 dimensional box which represents part of the atmosphere, but I do not want to have to worry about boundary conditions in the horizontal condition.


This is currently only supported in 1D sorry.

One way to do this is the following:

. Make a torus mesh (now you have a periodic mesh with the right topology but the wrong coordinates)

. Build a VectorFunctionSpace(m, 'DG', 1, dim=2) on it

Write a par_loop that transforms the torus coordinates into the flat coords of the square you want and replace the mesh's coordinates with these new coords.

c.f. for example https://bitbucket.org/colinjcotter/slicemodels/src/b6d5eac9dbf28cbcf24aef5be60e2c5756d0b677/slicemodels.py?at=master#cl-199 for a 1D example.

Lawrence
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