Add inlet/outlet BCs for the 2D-SWE

[patrickersing]

This PR implements inlet/outlet boundary conditions for the ShallowWaterEquationsWetDry2D.
The new boundary conditions BoundaryConditionWaterHeight and BoundaryConditionMomentum specify the water height or the momentum on the boundary and extrapolate the remaining quantity from the Riemann Invariant.

[codecov]

Codecov Report

Attention: Patch coverage is 98.04688% with 5 lines in your changes missing coverage. Please review.

Project coverage is 99.23%. Comparing base (009d14e) to head (d3fd8ff).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
...dgsem/elixir_shallowwater_moving_water_subsonic.jl	88.00%	3 Missing ⚠️
...1d_dgsem/elixir_shallowwater_moving_water_shock.jl	97.06%	1 Missing ⚠️
...gsem/elixir_shallowwater_moving_water_transonic.jl	96.67%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #91      +/-   ##
==========================================
- Coverage   99.33%   99.23%   -0.10%     
==========================================
  Files          66       71       +5     
  Lines        3115     3370     +255     
==========================================
+ Hits         3094     3344     +250     
- Misses         21       26       +5     

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[andrewwinters5000]

Thanks for adding this flexible boundary condition capability! It should work directly in 1D, right? It would be good to add an example elixir on TreeMesh if that is the case.

[patrickersing]

Thanks for adding this flexible boundary condition capability! It should work directly in 1D, right? It would be good to add an example elixir on TreeMesh if that is the case.

@andrewwinters5000 Yes, this should directly carry over to the 1D case. I only need to implement the boundary condition functions in ShallowWaterEquationsWetDry1D. I was planning to split this off into a separate PR, but I can of course also add this directly here.

[patrickersing]

There are some uncovered lines from the inverse_transform functions included in the elixirs. I would either keep it as it is and accept the uncovered lines, since they only occur in the elixir, or move the inverse_transform function to the shallow_water_equations_wet_dry.1d and add proper tests. However, since the function will only be used for these steady-state setups I am not sure if it makes sense to add the function to the code.

[andrewwinters5000]

Looks very nice, I just left some comments mainly regarding coding style.

[andrewwinters5000]

LGTM!

[andrewwinters5000]

There are some uncovered lines from the inverse_transform functions included in the elixirs. I would either keep it as it is and accept the uncovered lines, since they only occur in the elixir, or move the inverse_transform function to the shallow_water_equations_wet_dry.1d and add proper tests. However, since the function will only be used for these steady-state setups I am not sure if it makes sense to add the function to the code.

I agree that it makes more sense to leave the function definition of inverse_transform in the elixirs where it is needed for these special test case setups. Also, losing the (very) small coverage percentage is warranted in this case.