Add implementation of subcell bounds check

[bennibolm]

This PR adds the implementation of a subcell local bounds check. Rn, now it only contains the check for positivity bounds since it's the only feature merged to main.

It is implemented as a stage callback. Therefore, the solution before the convex combination in the SSPRK method is checked. This is sufficient since it is a convex combination and the previous solution is already checked.
BUT: The stage callback has to be called after SubcellLimiterIDPCorrection to obtain a meaningful test.

At the end of the simulation, the following output is added:

────────────────────────────────────────────────────────────────────────────────────────────────────
Maximum deviation from bounds:
────────────────────────────────────────────────────────────────────────────────────────────────────
rho1:
- positivity: 2.220446049250313e-16
rho2:
- positivity: 3.122502256758253e-17
────────────────────────────────────────────────────────────────────────────────────────────────────

If save_errors=true the deviations of the last stage in every time step is saved into a text file.

I just found an error in a note in the docstring of SubcellLimiterIDP. If the correction stage callback is no enabled, we do not get a DGSEM but a FV scheme. I fixed it in this PR.

[github-actions]

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[codecov]

Codecov Report

Attention: 84 lines in your changes are missing coverage. Please review.

Comparison is base (bb60b5d) 86.47% compared to head (f4f4146) 87.21%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1672      +/-   ##
==========================================
+ Coverage   86.47%   87.21%   +0.73%     
==========================================
  Files         423      425       +2     
  Lines       34312    34379      +67     
==========================================
+ Hits        29671    29981     +310     
+ Misses       4641     4398     -243     

Flag	Coverage Δ
unittests	87.21% <0.00%> (+0.73%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files	Coverage Δ
...ee_2d_dgsem/elixir_euler_shockcapturing_subcell.jl	0.00% <ø> (-100.00%)	⬇️
..._shock_bubble_shockcapturing_subcell_positivity.jl	0.00% <ø> (-100.00%)	⬇️
src/Trixi.jl	43.48% <ø> (ø)
src/solvers/dgsem_tree/subcell_limiters.jl	29.41% <0.00%> (-55.88%)	⬇️
src/solvers/dgsem_tree/subcell_limiters_2d.jl	0.00% <0.00%> (-94.34%)	⬇️
src/callbacks_stage/subcell_bounds_check_2d.jl	0.00% <0.00%> (ø)
src/callbacks_stage/subcell_bounds_check.jl	0.00% <0.00%> (ø)

... and 107 files with indirect coverage changes

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[bennibolm]

The implementation for exporting the deviations when save_errors=true is not tested right now. Should I activate it in one elixir to change this?
More general: Is this feature even wanted in main? For me, it was very helpful to have more information than the final maximum deviations, which is printed in the console at the end of a simulation.

[sloede]

The implementation for exporting the deviations when save_errors=true is not tested right now. Should I activate it in one elixir to change this? More general: Is this feature even wanted in main? For me, it was very helpful to have more information than the final maximum deviations, which is printed in the console at the end of a simulation.

I think everything that is useful for a future scientist/developer/debugger would make sense to keep. And yes, if you want to keep it, you should at least use it and check that a file was actually created.

[bennibolm]

The implementation for exporting the deviations when save_errors=true is not tested right now. Should I activate it in one elixir to change this? More general: Is this feature even wanted in main? For me, it was very helpful to have more information than the final maximum deviations, which is printed in the console at the end of a simulation.

I think everything that is useful for a future scientist/developer/debugger would make sense to keep. And yes, if you want to keep it, you should at least use it and check that a file was actually created.

I added a test to check the output file. Is that okay like this or am I missing something? @sloede
Unfortunately, both existing tests have maximum deviations of 0.0. I think I will change the tested elixir in the future. But at least, it is tested, that the file exists and the time steps and final time match.

[efaulhaber]

Idk, I can't really say much about this PR. I would have to spend more time to really work myself through the details.