Add bottom topography and Coriolis terms to 3D Cartesian SWE, and incorporate additional test cases

[amrueda]

This PR implements bottom topography non-conservative terms and Coriolis sources for the 3D shallow water equations in Cartesian form, which are used to simulate shallow water flows on curved manifolds, such as spherical shells. Additionally, we adapt the tests added in #58 to the 3D shallow water system.

Solution for the isolated mountain test at t = 15days:

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.11%. Comparing base (bbe4872) to head (69475ad).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #53      +/-   ##
==========================================
+ Coverage   90.68%   91.11%   +0.43%     
==========================================
  Files          22       22              
  Lines        2189     2228      +39     
==========================================
+ Hits         1985     2030      +45     
+ Misses        204      198       -6     

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[amrueda]

Convergence test for examples/elixir_shallowwater_cartesian_geostrophic_balance.jl:

• polydeg = 3:

####################################################################################################
l2
h                   h_v1                h_v2                h_v3                b                   
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
4.23e-01  -         1.41e+02  -         1.41e+02  -         4.55e+01  -         0.00e+00  -         
1.82e-02  4.54      1.16e+01  3.60      1.16e+01  3.60      3.80e+00  3.58      0.00e+00  NaN       
7.92e-04  4.52      9.23e-01  3.66      9.23e-01  3.66      3.66e-01  3.37      0.00e+00  NaN       

mean      4.53      mean      3.63      mean      3.63      mean      3.48      mean      NaN       
----------------------------------------------------------------------------------------------------
linf
h                   h_v1                h_v2                h_v3                b                   
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
3.29e+00  -         6.17e+02  -         6.17e+02  -         2.71e+02  -         0.00e+00  -         
1.64e-01  4.32      6.55e+01  3.24      6.55e+01  3.24      3.78e+01  2.85      0.00e+00  NaN       
8.25e-03  4.32      5.36e+00  3.61      5.36e+00  3.61      4.10e+00  3.20      0.00e+00  NaN       

mean      4.32      mean      3.42      mean      3.42      mean      3.02      mean      NaN       
----------------------------------------------------------------------------------------------------

• polydeg = 4:

####################################################################################################
l2
h                   h_v1                h_v2                h_v3                b                   
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
1.95e-02  -         1.67e+01  -         1.67e+01  -         5.39e+00  -         0.00e+00  -         
5.41e-04  5.17      7.51e-01  4.47      7.51e-01  4.47      2.76e-01  4.29      0.00e+00  NaN       
1.86e-05  4.86      3.55e-02  4.40      3.55e-02  4.40      1.24e-02  4.48      0.00e+00  NaN       

mean      5.02      mean      4.44      mean      4.44      mean      4.38      mean      NaN       
----------------------------------------------------------------------------------------------------
linf
h                   h_v1                h_v2                h_v3                b                   
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
9.67e-02  -         1.40e+02  -         1.40e+02  -         4.41e+01  -         0.00e+00  -         
4.71e-03  4.36      6.86e+00  4.36      6.86e+00  4.36      2.21e+00  4.32      0.00e+00  NaN       
2.10e-04  4.49      3.42e-01  4.32      3.42e-01  4.32      1.01e-01  4.45      0.00e+00  NaN       

mean      4.42      mean      4.34      mean      4.34      mean      4.38      mean      NaN       
----------------------------------------------------------------------------------------------------

[tristanmontoya]

Nice work; nothing that stands out to me as needing changes at this point. If you're fine with it, then I would say LGTM.