Add elixir for shallow water equations with P4estMesh

[JoshuaLampert]

Currently, there is no elixir for the shallow water equations on a P4estMesh. So, I thought I add a basic one. As also stated here this currently does not work with MPI. Once, this is resolved we could add this elixir also to the test_mpi_p4est_2d.jl.

[andrewwinters5000]

Thanks for adding this! Just be cautious here that one should not use AMR with the shallow water equations at the moment because the numerical scheme will not be well-balanced due to how the mortars are currently computed. Special mortar projections are required to keep the overall solver well-balanced. This was one reason I had yet to make any kind of shallow water elixir for the P4estMesh.

[ranocha]

Thanks! It looks like the new tests are failing. Could you also please consider using a less refined mesh to save CI time?

[JoshuaLampert]

Ok, so maybe we wait with this to be merged until AMR will keep the scheme well-balanced for a P4estMesh?

[ranocha]

Thanks! I think it's fine to merge this as it is since we could get the same problem with AMR when using the TreeMesh - where the shallow water equations should work. Thus, I think we can merge this PR when tests pass - unless @andrewwinters5000 has another opinion.

[codecov]

Codecov Report

Merging #1424 (dadd8cc) into main (5133c36) will not change coverage.
The diff coverage is n/a.

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##             main    #1424   +/-   ##
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  Coverage   95.74%   95.74%           
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  Files         356      356           
  Lines       29598    29598           
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  Hits        28338    28338           
  Misses       1260     1260           

Flag	Coverage Δ
unittests	95.74% <ø> (ø)

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[andrewwinters5000]

LGTM! This will be good to have for MPI testing.