Use total pressure for 1D HLLC MHD

[DanielDoehring]

Unfortunately I made a mistake in the PR https://github.com/trixi-framework/Trixi.jl/pull/1702 by not noticing the different notions of pressure $p$ (thermal in https://www.sciencedirect.com/science/article/pii/S0021999118301463 ) and total $$p = p_\mathrm{Thermal} + \frac{1}{2} \Vert \boldsymbol B \Vert^2 $$ in https://www.sciencedirect.com/science/article/pii/S0021999104003857 . This PR takes care of this.

For validation the Alfven test is performed for

flux_lax_friedrichs:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_v3              rho_e               B1                  B2                  B3                  
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
1.04e-05  -         6.57e-07  -         3.58e-05  -         3.58e-05  -         5.08e-06  -         1.20e-16  -         3.60e-05  -         3.60e-05  -         
1.99e-07  5.71      4.27e-09  7.26      1.87e-06  4.26      1.87e-06  4.26      9.38e-08  5.76      1.20e-16  -0.00     1.88e-06  4.26      1.88e-06  4.26      
3.23e-09  5.94      1.47e-11  8.19      1.12e-07  4.07      1.12e-07  4.07      1.41e-09  6.06      1.20e-16  0.00      1.12e-07  4.07      1.12e-07  4.07      
5.11e-11  5.98      7.38e-14  7.64      6.90e-09  4.02      6.90e-09  4.02      2.23e-11  5.98      1.20e-16  0.00      6.90e-09  4.02      6.90e-09  4.02      
8.02e-13  5.99      1.80e-14  2.04      4.30e-10  4.00      4.30e-10  4.00      3.49e-13  6.00      1.20e-16  -0.00     4.30e-10  4.00      4.30e-10  4.00      

mean      5.91      mean      6.28      mean      4.09      mean      4.09      mean      5.95      mean      0.00      mean      4.09      mean      4.09      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_v3              rho_e               B1                  B2                  B3                  
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
2.61e-05  -         9.58e-07  -         1.24e-04  -         1.24e-04  -         1.51e-05  -         2.22e-16  -         1.27e-04  -         1.27e-04  -         
5.70e-07  5.52      8.61e-09  6.80      6.41e-06  4.28      6.41e-06  4.28      2.68e-07  5.82      2.22e-16  -0.00     6.41e-06  4.30      6.41e-06  4.30      
9.45e-09  5.91      2.41e-11  8.48      2.90e-07  4.46      2.90e-07  4.46      4.20e-09  5.99      2.22e-16  -0.00     2.90e-07  4.46      2.90e-07  4.46      
1.50e-10  5.98      1.72e-13  7.13      1.40e-08  4.37      1.40e-08  4.37      6.62e-11  5.99      2.22e-16  -0.00     1.40e-08  4.37      1.40e-08  4.37      
2.36e-12  5.99      2.11e-14  3.03      7.43e-10  4.24      7.43e-10  4.24      1.04e-12  5.99      2.22e-16  -0.00     7.43e-10  4.24      7.43e-10  4.24      

mean      5.85      mean      6.36      mean      4.34      mean      4.34      mean      5.95      mean      -0.00     mean      4.34      mean      4.34      
----------------------------------------------------------------------------------------------------

flux_hll:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_v3              rho_e               B1                  B2                  B3                  
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
1.04e-05  -         6.57e-07  -         3.58e-05  -         3.58e-05  -         5.08e-06  -         1.20e-16  -         3.60e-05  -         3.60e-05  -         
1.99e-07  5.71      4.27e-09  7.26      1.87e-06  4.26      1.87e-06  4.26      9.38e-08  5.76      1.20e-16  -0.00     1.88e-06  4.26      1.88e-06  4.26      
3.23e-09  5.94      1.47e-11  8.19      1.12e-07  4.07      1.12e-07  4.07      1.41e-09  6.06      1.20e-16  0.00      1.12e-07  4.07      1.12e-07  4.07      
5.11e-11  5.98      7.39e-14  7.63      6.90e-09  4.02      6.90e-09  4.02      2.23e-11  5.98      1.20e-16  0.00      6.90e-09  4.02      6.90e-09  4.02      
8.02e-13  5.99      1.80e-14  2.04      4.30e-10  4.00      4.30e-10  4.00      3.49e-13  6.00      1.20e-16  -0.00     4.30e-10  4.00      4.30e-10  4.00      

mean      5.91      mean      6.28      mean      4.09      mean      4.09      mean      5.95      mean      0.00      mean      4.09      mean      4.09      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_v3              rho_e               B1                  B2                  B3                  
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
2.61e-05  -         9.58e-07  -         1.24e-04  -         1.24e-04  -         1.51e-05  -         2.22e-16  -         1.27e-04  -         1.27e-04  -         
5.70e-07  5.52      8.61e-09  6.80      6.41e-06  4.28      6.41e-06  4.28      2.68e-07  5.82      2.22e-16  -0.00     6.41e-06  4.30      6.41e-06  4.30      
9.45e-09  5.91      2.41e-11  8.48      2.90e-07  4.46      2.90e-07  4.46      4.20e-09  5.99      2.22e-16  -0.00     2.90e-07  4.46      2.90e-07  4.46      
1.50e-10  5.98      1.72e-13  7.13      1.40e-08  4.37      1.40e-08  4.37      6.62e-11  5.99      2.22e-16  -0.00     1.40e-08  4.37      1.40e-08  4.37      
2.37e-12  5.98      2.24e-14  2.94      7.43e-10  4.24      7.43e-10  4.24      1.04e-12  5.99      2.22e-16  -0.00     7.43e-10  4.24      7.43e-10  4.24      

mean      5.85      mean      6.34      mean      4.34      mean      4.34      mean      5.95      mean      -0.00     mean      4.34      mean      4.34      
----------------------------------------------------------------------------------------------------

flux_hllc:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_v3              rho_e               B1                  B2                  B3                  
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
1.04e-05  -         1.97e-06  -         3.59e-05  -         3.59e-05  -         5.27e-06  -         1.20e-16  -         3.60e-05  -         3.60e-05  -         
2.08e-07  5.64      3.27e-08  5.91      1.87e-06  4.26      1.87e-06  4.26      8.80e-08  5.90      1.20e-16  -0.00     1.87e-06  4.26      1.87e-06  4.26      
4.02e-09  5.69      5.72e-10  5.84      1.12e-07  4.07      1.12e-07  4.07      1.40e-09  5.97      1.20e-16  0.00      1.12e-07  4.07      1.12e-07  4.07      
9.57e-11  5.39      8.64e-12  6.05      6.90e-09  4.02      6.90e-09  4.02      2.18e-11  6.01      1.20e-16  0.00      6.90e-09  4.02      6.90e-09  4.02      
2.73e-12  5.13      1.37e-13  5.98      4.30e-10  4.00      4.30e-10  4.00      3.37e-13  6.02      1.20e-16  -0.00     4.30e-10  4.00      4.30e-10  4.00      

mean      5.46      mean      5.94      mean      4.09      mean      4.09      mean      5.97      mean      0.00      mean      4.09      mean      4.09      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_v3              rho_e               B1                  B2                  B3                  
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
2.89e-05  -         7.31e-06  -         1.24e-04  -         1.24e-04  -         1.51e-05  -         2.22e-16  -         1.26e-04  -         1.26e-04  -         
7.75e-07  5.22      1.06e-07  6.11      6.42e-06  4.27      6.42e-06  4.27      2.61e-07  5.86      2.22e-16  -0.00     6.39e-06  4.30      6.39e-06  4.30      
1.71e-08  5.50      1.56e-09  6.08      2.90e-07  4.47      2.90e-07  4.47      4.12e-09  5.98      2.22e-16  -0.00     2.90e-07  4.46      2.90e-07  4.46      
4.05e-10  5.40      2.61e-11  5.90      1.40e-08  4.37      1.40e-08  4.37      6.41e-11  6.00      2.22e-16  -0.00     1.40e-08  4.37      1.40e-08  4.37      
1.06e-11  5.26      3.93e-13  6.06      7.43e-10  4.24      7.43e-10  4.24      9.86e-13  6.02      2.22e-16  -0.00     7.43e-10  4.24      7.43e-10  4.24      

mean      5.34      mean      6.04      mean      4.34      mean      4.34      mean      5.97      mean      -0.00     mean      4.34      mean      4.34      
----------------------------------------------------------------------------------------------------

[github-actions]

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[andrewwinters5000]

LGTM! Just a small suggestion updating the new comment to avoid future confusion.

[codecov]

Codecov Report

Attention: 1 lines in your changes are missing coverage. Please review.

Comparison is base (d7e1f74) 94.31% compared to head (eb006ff) 85.21%.

Files	Patch %	Lines
src/equations/ideal_glm_mhd_1d.jl	80.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1756      +/-   ##
==========================================
- Coverage   94.31%   85.21%   -9.10%     
==========================================
  Files         431      431              
  Lines       34893    34845      -48     
==========================================
- Hits        32908    29692    -3216     
- Misses       1985     5153    +3168     

Flag	Coverage Δ
unittests	85.21% <80.00%> (-9.10%)	⬇️

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[andrewwinters5000]

LGTM!