First PR for 3D subcell limiting

[bennibolm]

This PR contains 3D subcell limiting for P4estMesh:

• only positivity limiter for conservative variables
• no support for equations with nonconservative terms yet

Convergence test with polynomial degree of 4:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_v3              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
3.97e-03  -         4.22e-03  -         4.31e-03  -         3.99e-03  -         8.09e-03  -         
1.96e-04  4.34      2.24e-04  4.24      2.23e-04  4.27      1.40e-04  4.83      4.12e-04  4.30      
6.63e-06  4.89      7.37e-06  4.92      7.36e-06  4.92      4.32e-06  5.02      1.38e-05  4.90      
1.71e-07  5.28      1.78e-07  5.37      1.76e-07  5.39      1.20e-07  5.17      3.51e-07  5.29      

mean      4.83      mean      4.84      mean      4.86      mean      5.01      mean      4.83      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_v3              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
3.91e-02  -         3.21e-02  -         4.75e-02  -         4.77e-02  -         1.00e-01  -         
1.77e-03  4.46      1.91e-03  4.07      1.98e-03  4.58      1.63e-03  4.87      4.33e-03  4.53      
6.36e-05  4.80      6.22e-05  4.94      7.62e-05  4.70      5.85e-05  4.80      1.44e-04  4.91      
3.71e-06  4.10      3.46e-06  4.17      4.42e-06  4.11      3.58e-06  4.03      7.92e-06  4.18      

mean      4.45      mean      4.39      mean      4.46      mean      4.57      mean      4.54      
----------------------------------------------------------------------------------------------------

used the following mesh

Example of the sedov blast (see elixir): I used a easier setup with pressure 0.1 since only positivity limiting of density can be used.
On the left: Simulation in 3d. I adapted the initial condition such that nothing happens in the third direction.
On the right: Simulation in 2d

video.mp4

There are very small differences between the simulations, but I would say that this is expected.

[github-actions]

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[codecov]

Codecov Report

❌ Patch coverage is 97.72727% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.81%. Comparing base (1d75f8f) to head (5f271e7).

Files with missing lines	Patch %	Lines
src/solvers/dgsem_p4est/subcell_limiters_3d.jl	90.00%	3 Missing ⚠️
...llbacks_stage/subcell_limiter_idp_correction_3d.jl	97.30%	1 Missing ⚠️
src/solvers/dgsem_p4est/dg_3d_subcell_limiters.jl	99.24%	1 Missing ⚠️
src/solvers/dgsem_tree/containers_3d.jl	98.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2582      +/-   ##
==========================================
+ Coverage   96.81%   96.81%   +0.01%     
==========================================
  Files         535      539       +4     
  Lines       42813    43077     +264     
==========================================
+ Hits        41446    41704     +258     
- Misses       1367     1373       +6     

Flag	Coverage Δ
unittests	96.81% <97.73%> (+0.01%)	⬆️

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[DanielDoehring]

I will take a closer look at the code this afternoon.

Could you maybe run one more refinement step of the convergence test (If it takes not too much time)?

[DanielDoehring]

Most of my comments are aiming for consistent formatting & asking for some comments. The implementation itself looks sound to me. Would be good to add a test (not necessarily an additional elixir) with AMR to stress-test the resize!ing

[bennibolm]

I will take a closer look at the code this afternoon.

Could you maybe run one more refinement step of the convergence test (If it takes not too much time)?

Thank you very much.
I added one more step to the table above. The l2 error looks good, while the linf error drops a bit. This last simulation already took over an hour.

I will work through the suggestions in the next couple of hours. Thank you!

[DanielDoehring]

Good to go from my side!