Add call to the positivity limiter after coarsen / refine

[andrewwinters5000]

This PR re-implements max_abs_speeds for the time step calculation that uses Base.sqrt. Also, specialized refine! and coarsen! functions are implemented to ensure positivity of the water height after adaptation in the AMR callback. There were negative water heights generated (for example in the coarsening step) in wet/dry transition areas.

[codecov]

Codecov Report

Attention: Patch coverage is 97.50000% with 2 lines in your changes missing coverage. Please review.

Project coverage is 99.19%. Comparing base (464ac24) to head (a8d77a6).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/callbacks_step/amr_dg2d.jl	97.37%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #97      +/-   ##
==========================================
- Coverage   99.23%   99.19%   -0.04%     
==========================================
  Files          71       72       +1     
  Lines        3370     3449      +79     
==========================================
+ Hits         3344     3421      +77     
- Misses         26       28       +2     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[andrewwinters5000]

The missed lines are due to the fact that we do not run anything with MPI in the CI testing. This could be added (I think) relatively easily. It might be good to run a couple tests in parallel in TrixiSW to make sure that this capability is still available.

[andrewwinters5000]

Nevermind, there is no calc_mpi_interface_flux with nonconservative::True() implemented in Trixi. So adding such a test is outside the scope of this PR. We will have to live with the ≈0.16% drop in coverage for these six untested lines. Or we could comment them out with a note about what needs done for MPI + noncons + Trixi.

[patrickersing]

Thanks for fixing the AMR test. Hopefully, this will also make the AMR procedure more robust.
The implementation looks good to me, I just left suggestions for some of the comments.

[DanielDoehring]

Would it be possible to extend this to the main repository?

[patrickersing]

LGTM!

[andrewwinters5000]

Would it be possible to extend this to the main repository?

I agree that this is something that should be done in main repo to address trixi-framework/Trixi.jl#2064.

I thought about this but I could not figure out a proper and equation agnostic way to have the call to the limiter. For shallow water I know that we always want to limit the water height and that the threshold lives in the equations such that I could hard code the limiter variable in the call

   # Apply limiter to ensure admissible solution states
    limiter_shallow_water!(u, equations.threshold_limiter, waterheight,
                           mesh, equations, dg, cache)

However, for something like compressible Euler one would limit the density and pressure but (potentially) with different threshold values. Because the AMR callback does not "know" about the stage limiter callback it is difficult to extract this information.