Add wet/dry functionality for the Multilayer SWE in 1D

[patrickersing]

This PR adds wet/dry functionality to the ShallowWaterMultiLayerEquations1D.

The new functionality includes support for shock-capturing, a positivity-limiter and the new hydrostatic_reconstruction_ersing_etal as well as corresponding tests and examples.

The general strategy follows the implementation of the ShallowWaterEquationsWetDry1D. However, in contrast to the ShallowWaterEquationsWetDry1D the positivity-limiter is applied layerwise and only acts on the water heights h (the momentum remains unchanged) and a velocity desingularization is applied to avoid numerical problems near dry states. The specific implementation of the positivity-limiter is still experimental and might change.

The new hydrostatic reconstruction can be used to create an entropy-stable and well-balanced scheme if the surface flux is set to

surface_flux = (FluxHydrostaticReconstruction(FluxPlusDissipation(flux_ersing_etal, DissipationLocalLaxFriedrichs()), hydrostatic_reconstruction_ersing_etal),
                FluxHydrostaticReconstruction(flux_nonconservative_ersing_etal, hydrostatic_reconstruction_ersing_etal))

[codecov]

Codecov Report

Attention: Patch coverage is 98.94180% with 2 lines in your changes are missing coverage. Please review.

Project coverage is 99.23%. Comparing base (2c9afa2) to head (dcb6abf).

Files	Patch %	Lines
...c/callbacks_stage/positivity_shallow_water_dg1d.jl	95.34%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #38      +/-   ##
==========================================
- Coverage   99.26%   99.23%   -0.04%     
==========================================
  Files          50       54       +4     
  Lines        2054     2228     +174     
==========================================
+ Hits         2039     2211     +172     
- Misses         15       17       +2     

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

[andrewwinters5000]

Nice work @patrickersing ! Having positivity across multiple layers is a great new feature. I left a few comments and opened a discuss about having different threshold quantities across the different variants of the wet/dry capabilities.

[andrewwinters5000]

It seems that the Mac CI tests are failing due to too strict tolerances. We should keep an eye on this because it would be very annoying (and concerning) if we need to soften the tolerances on so many tests.

[patrickersing]

It seems that the Mac CI tests are failing due to too strict tolerances. We should keep an eye on this because it would be very annoying (and concerning) if we need to soften the tolerances on so many tests

I have softened the tolerances in 2857753 and the CI now passes (at least in the recent run). I do not really see another alternative to fix the tests.
I also think the tolerance changes are reasonable. Only elixir_shallowwater_multilayer_beach.jl required a pretty high tolerance atol=1e-5, but this is in line with the tolerance atol=1e-7, set in elixir_shallowwater_beach.jl. The higher value is probably necessary, since the test runs until t=0.25 instead of t=0.05.

[andrewwinters5000]

Looks good overall @patrickersing ! The only hanging question is related to the (mysterious) reason why lines that should be covered are reported as uncovered.

[ranocha]

I am not sure why these lines are not reported as being covered. Any ideas @ranocha or @sloede ?

Because we never call real(equations) in a standard setup? I guess you could get also get rid of this if you don't use it

[patrickersing]

I am not sure why these lines are not reported as being covered. Any ideas @ranocha or @sloede ?

Because we never call real(equations) in a standard setup? I guess you could get also get rid of this if you don't use it

@ranocha These lines are definitely called during testing and the respective function calls also show up as covered, so we expect coverage. The same problem also appears for a similar function nlayers(equations).

[andrewwinters5000]

LGTM! The small coverage drop is due to spurious lines that should be reported as covered but are not as discussed above.