Navier-Stokes Test Case: Viscous Shock propagation

[DanielDoehring]

This PR adds elixirs for the Becker-Morduchow-Libby solution of a 1D viscous moving shock.
Can be used to test for convergence without source terms as for the manufactured solution test cases.

Convergence study for the 2D case:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       
3.76e-03  -         3.11e-03  -         8.27e-17  -         3.26e-03  -         
3.55e-04  3.41      2.45e-04  3.67      7.40e-16  -3.16     2.72e-04  3.58      
5.80e-05  2.61      2.92e-05  3.07      2.58e-11  -15.09    3.68e-05  2.89      
4.09e-06  3.82      1.93e-06  3.92      1.82e-11  0.51      2.45e-06  3.91      
2.50e-07  4.03      1.50e-07  3.69      6.79e-12  1.42      1.71e-07  3.84      

mean      3.47      mean      3.59      mean      -4.08     mean      3.56      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       
1.93e-02  -         1.39e-02  -         4.78e-16  -         1.50e-02  -         
2.20e-03  3.13      2.18e-03  2.67      4.80e-15  -3.33     2.00e-03  2.90      
7.49e-04  1.56      4.42e-04  2.30      7.95e-10  -17.34    5.24e-04  1.93      
5.00e-05  3.91      3.06e-05  3.85      6.66e-10  0.26      3.61e-05  3.86      
2.82e-06  4.15      1.91e-06  4.00      2.84e-10  1.23      2.25e-06  4.01      

mean      3.19      mean      3.21      mean      -4.80     mean      3.18      
----------------------------------------------------------------------------------------------------

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.37%. Comparing base (987fa7e) to head (9617641).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2173      +/-   ##
==========================================
+ Coverage   96.36%   96.37%   +0.01%     
==========================================
  Files         480      483       +3     
  Lines       38230    38329      +99     
==========================================
+ Hits        36840    36939      +99     
  Misses       1390     1390              

Flag	Coverage Δ
unittests	96.37% <100.00%> (+0.01%)	⬆️

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[ranocha]

CI fails: https://github.com/trixi-framework/Trixi.jl/actions/runs/11935430540/job/33266749164?pr=2173#step:7:9616

[DanielDoehring]

Yeah, for some reason there are allocations due to the boundary conditions. I hope I can figure it out...

[ranocha]

Yeah, for some reason there are allocations due to the boundary conditions. I hope I can figure it out...

You use a lot of global variables

[ranocha]

Thanks!

[DanielDoehring]

There is one thing I need to double-check before this should be merged

[DanielDoehring]

Alright good to go.

[andrewwinters5000]

LGTM!

[ranocha]

Thanks!