PERK4 standalone

[DanielDoehring]

This concludes (as of now) the set of standalone PERK methods.

Xref: #21

[github-actions]

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Created with ❤️ by the Trixi.jl community.

[DanielDoehring]

@warisa-r Can you take a first look?

[codecov]

Codecov Report

Attention: Patch coverage is 93.17269% with 17 lines in your changes missing coverage. Please review.

Project coverage is 96.40%. Comparing base (679e4c7) to head (3167a1b).

Files with missing lines	Patch %	Lines
...ation/paired_explicit_runge_kutta/methods_PERK4.jl	93.44%	8 Missing ⚠️
ext/TrixiConvexECOSExt.jl	89.71%	7 Missing ⚠️
...s/structured_2d_dgsem/elixir_euler_vortex_perk4.jl	95.45%	1 Missing ⚠️
...ation/paired_explicit_runge_kutta/methods_PERK3.jl	90.91%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #2147       +/-   ##
===========================================
+ Coverage   70.19%   96.40%   +26.21%     
===========================================
  Files         486      488        +2     
  Lines       39102    39362      +260     
===========================================
+ Hits        27445    37944    +10499     
+ Misses      11657     1418    -10239     

Flag	Coverage Δ
unittests	96.40% <93.17%> (+26.21%)	⬆️

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[warisa-r]

@warisa-r Can you take a first look?

I'm on it!

[warisa-r]

Here is what I get from the brief look! I hope I could be of some help. Some might be totally non-sensical or out of ignorance. Apologies in advance!

[DanielDoehring]

This should wait for #2180

[DanielDoehring]

Two more refinement runs for the isentropic vortex example:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       
1.85e-04  -         4.25e-04  -         3.72e-04  -         2.67e-03  -         
1.55e-05  3.58      3.22e-05  3.73      2.80e-05  3.73      2.15e-04  3.64      
9.85e-07  3.97      1.80e-06  4.16      1.85e-06  3.92      1.34e-05  4.00      

mean      3.78      mean      3.94      mean      3.83      mean      3.82      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       
2.50e-03  -         9.27e-03  -         9.88e-03  -         3.07e-02  -         
3.85e-04  2.70      7.86e-04  3.56      7.82e-04  3.66      5.33e-03  2.53      
2.52e-05  3.93      6.55e-05  3.59      6.78e-05  3.53      3.63e-04  3.88      

mean      3.32      mean      3.57      mean      3.59      mean      3.20      
----------------------------------------------------------------------------------------------------