Quad-Based Icosahedral Grid

[amrueda]

This PR implements a quad-based icosahedral grid of the sphere as a P4estMesh{2}. The mesh has 60 * trees_per_face_dimension^2 trees: 20 triangular faces of the icosahedron, each subdivided into 3 parent quads, each of which subdivided into trees_per_face_dimension^2 trees.

The following convergence results can be obtained using:

julia> convergence_test("../examples/elixir_shallowwater_quad_icosahedron_shell_advection.jl", 4, cells_per_dimension = (1,1), polydeg = 3)

####################################################################################################
l2
h                   h_v1                h_v2                h_v3                b                   
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
7.24e+00  -         2.87e-05  -         1.40e-05  -         2.87e-05  -         0.00e+00  -         
4.57e-01  3.99      1.85e-06  3.95      6.77e-07  4.37      1.85e-06  3.95      0.00e+00  NaN       
3.94e-02  3.53      1.62e-07  3.51      4.39e-08  3.95      1.62e-07  3.51      0.00e+00  NaN       
3.02e-03  3.70      1.25e-08  3.70      2.95e-09  3.90      1.25e-08  3.70      0.00e+00  NaN       

mean      3.74      mean      3.72      mean      4.07      mean      3.72      mean      NaN       
----------------------------------------------------------------------------------------------------
linf
h                   h_v1                h_v2                h_v3                b                   
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
7.33e+01  -         3.15e-04  -         1.77e-04  -         3.15e-04  -         0.00e+00  -         
1.36e+01  2.43      5.73e-05  2.46      1.47e-05  3.59      5.73e-05  2.46      0.00e+00  NaN       
1.67e+00  3.02      7.05e-06  3.02      1.81e-06  3.02      7.05e-06  3.02      0.00e+00  NaN       
1.33e-01  3.66      5.59e-07  3.66      1.44e-07  3.66      5.59e-07  3.66      0.00e+00  NaN       

mean      3.04      mean      3.05      mean      3.42      mean      3.05      mean      NaN       
----------------------------------------------------------------------------------------------------

Advection_IcosahedralGrid.mp4

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 89.56%. Comparing base (07d698e) to head (4a13720).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #50      +/-   ##
==========================================
+ Coverage   87.56%   89.56%   +2.00%     
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  Files          18       19       +1     
  Lines        1447     1706     +259     
==========================================
+ Hits         1267     1528     +261     
+ Misses        180      178       -2     

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[tristanmontoya]

LGTM! The failing test is unrelated to these changes, see trixi-framework/Trixi.jl#2185 (comment).