Sc/mhd treemesh 3d

[SimonCan]

This branch is a fork of the ns-treemesh-3d branch. It implements the compressible visco-resistive MHD equations in 3 dimensions on the treemesh.

This is a todo list before we can merge with the main branch:

• Perform tests on different systems, like Alfven waves, Kelvin-Helmholtz suppression and dynamos.
• Write tests.
• Add at least one more example elixir with source term that captures Ohmic heating. Perhaps a dynamo is a good example for this.

Convergence test for examples/tree_3d_dgsem/elixir_mhd_diffusive_alfven_wave.jl:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_v3              rho_e               B1                  B2                  B3                  psi                 
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
5.18e-03  -         1.33e-02  -         7.05e-03  -         1.65e-02  -         7.92e-03  -         1.29e-02  -         7.94e-03  -         1.65e-02  -         3.19e-03  -         
4.71e-04  3.46      8.07e-04  4.04      4.63e-04  3.93      9.26e-04  4.15      2.71e-04  4.87      8.33e-04  3.96      4.16e-04  4.25      9.26e-04  4.15      3.07e-04  3.38      
2.54e-05  4.21      7.02e-05  3.52      3.80e-05  3.61      8.17e-05  3.50      1.49e-05  4.18      7.15e-05  3.54      4.46e-05  3.22      7.99e-05  3.53      3.19e-05  3.27      

mean      3.84      mean      3.78      mean      3.77      mean      3.83      mean      4.53      mean      3.75      mean      3.74      mean      3.84      mean      3.32      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_v3              rho_e               B1                  B2                  B3                  psi                 
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
1.15e-02  -         3.24e-02  -         1.86e-02  -         5.63e-02  -         3.32e-02  -         4.28e-02  -         2.85e-02  -         5.62e-02  -         1.66e-02  -         
9.95e-04  3.53      3.09e-03  3.39      1.65e-03  3.49      3.55e-03  3.99      1.20e-03  4.79      3.44e-03  3.64      1.77e-03  4.00      3.53e-03  3.99      1.03e-03  4.00      
5.39e-05  4.21      2.58e-04  3.58      1.25e-04  3.72      3.01e-04  3.56      4.74e-05  4.66      2.62e-04  3.72      1.81e-04  3.29      2.73e-04  3.69      6.51e-05  3.99      

mean      3.87      mean      3.49      mean      3.61      mean      3.77      mean      4.73      mean      3.68      mean      3.65      mean      3.84      mean      4.00      
----------------------------------------------------------------------------------------------------
Dict{Symbol, Any} with 3 entries:
  :variables => ("rho", "rho_v1", "rho_v2", "rho_v3", "rho_e", "B1", "B2", "B3", "psi")
  :l2        => [3.83558, 3.78294, 3.7685, 3.8284, 4.52743, 3.74941, 3.73793, 3.84348, 3.32303]
  :linf      => [3.8669, 3.48655, 3.60754, 3.7739, 4.72625, 3.67685, 3.64742, 3.84359, 3.9968]

[SimonCan]

Corrected the convergence tests. Seems to have improved the convergence rate.