p4est solver on a spherical mesh

[amrueda]

This PR implements a version of the 2D p4est solver that runs on a spherical shell that is constructed from a cubed sphere. Since there are three Cartesian space dimensions on the surface of the sphere, we use the 2D p4est solver in combination with a 3D equation.

The connectivities are inherited from the p8est 3D cubed-sphere implementation, but they are adapted to p4est (2D). The discretization strategy follows the approach by:

• Giraldo (2001). A spectral element shallow water model on spherical geodesic grids. http://faculty.nps.edu/fxgirald/Homepage/Publications_files/Giraldo_IJNMF_2001.pdf.

The following visualization uses this version of Trixi2Vtk:

earth.mp4

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 258 lines in your changes missing coverage. Please review.

Project coverage is 19.32%. Comparing base (7241ff6) to head (bb2b1b2).
Report is 1 commits behind head on main.

Files	Patch %	Lines
src/meshes/p4est_cubed_sphere.jl	0.00%	153 Missing ⚠️
...olvers/dgsem_p4est/containers_2d_manifold_in_3d.jl	0.00%	77 Missing ⚠️
...vers/dgsem_p4est/dg_2d_manifold_in_3d_cartesian.jl	0.00%	20 Missing ⚠️
...semidiscretization_hyperbolic_2d_manifold_in_3d.jl	0.00%	5 Missing ⚠️
src/solvers/dgsem_p4est/dg.jl	0.00%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #25      +/-   ##
==========================================
- Coverage   28.07%   19.32%   -8.75%     
==========================================
  Files           3        8       +5     
  Lines         570      828     +258     
==========================================
  Hits          160      160              
- Misses        410      668     +258     

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[tristanmontoya]

I've added my covariant solver to this PR in https://github.com/trixi-framework/TrixiAtmo.jl/tree/tm/p4est_new_container

[tristanmontoya]

@amrueda I think we can merge this even if the dimension check isn't removed from the main Trixi.jl package yet, since my covariant solver will use it.

[tristanmontoya]

I'm going to merge this now; tests will be added for the Cartesian solver once the dimension check in Trixi.jl is moved out of the inner constructor for SemidiscretizationHyperbolic.

[ranocha]

I'm going to merge this now; tests will be added for the Cartesian solver once the dimension check in Trixi.jl is moved out of the inner constructor for SemidiscretizationHyperbolic.

The new version of Trixi.jl including the fix is released

[tristanmontoya]

I'm going to merge this now; tests will be added for the Cartesian solver once the dimension check in Trixi.jl is moved out of the inner constructor for SemidiscretizationHyperbolic.

The new version of Trixi.jl including the fix is released

Great, thank you!