Two-layer shallow water equations

[patrickersing]

This adds an implementation for the two-layer shallow water equations with entropy conservative and entropy stable fluxes in 1D and 2D. The changes include:

• 1D equations for Tree mesh
• 2D equations for Tree mesh & Unstructured mesh
• Initial condition & source terms for a manufactured solution
• A slip-wall boundary condition (for Tree mesh in 1D & Unstructured mesh in 2D)
• Example elixirs for convergence, well-balancedness and a dam break
• Test files for the new features

[andrewwinters5000]

I am still working on my full review. But these two suggestions I believe will fix the broken tests due to the breaking changes introduced with Trixi v0.5. Is that right @ranocha ?

[ranocha]

I am still working on my full review. But these two suggestions I believe will fix the broken tests due to the breaking changes introduced with Trixi v0.5. Is that right @ranocha ?

Yes, looks correct 👍

[andrewwinters5000]

Overall very nice work! This is a nice new set of equations to expand the capabilities of Trixi. A lot of my comments / suggestions are for cleanup of the elixirs. There are some naming conventions for the new equations that we need to decide on as well.

[ranocha]

@andrewwinters5000 Please feel free to request a review from me once your comments are addressed

[andrewwinters5000]

Nice work overall! All my original comments were addressed. I left some additional comments, most of which are just spacing adjustments.

[andrewwinters5000]

LGTM! I just noted two small typos in the docstrings that need corrected. Also, @patrickersing you should add yourself to the AUTHORS.md list of contributors.

[sloede]

Does this also work for P4estMesh2D? Or is it "in general yes, but we haven't tried it yet"?

[sloede]

I did a not-in-super-depth review of this PR and mostly it LGTM. I've left a few comments, most of them on consistency and most of them thought as suggestions. I did not review the 1D part, but anything in 2D that affects a similar place in 1D should be considered for a change as well...

[sloede]

Does this also work for P4estMesh2D? Or is it "in general yes, but we haven't tried it yet"?

Please let me know if I should review something more in depth or have a look at something in particular!

[andrewwinters5000]

Does this also work for P4estMesh2D? Or is it "in general yes, but we haven't tried it yet"?

It could easily be adapted to work with the P4estMesh2D file format. This is not a problem. The main issue is that the AMR as it is currently implemented will not be well-balanced for these equations (neither for the original shallow water equations). The mortar projections would need to be done in a special way to allow for AMR meshes. This has been on my TODO list for sometime but I would propose it get separated to a different PR.

[sloede]

This has been on my TODO list for sometime but I would propose it get separated to a different PR.

Yes, that absolutely makes sense to separate from the current PR. Looking forward to review well-balanaced AMR :-)

[sloede]

LGTM, thanks!

[codecov]

Codecov Report

Merging #1297 (f2c6c43) into main (cc2cda4) will increase coverage by 13.23%.
The diff coverage is 99.29%.

@@             Coverage Diff             @@
##             main    #1297       +/-   ##
===========================================
+ Coverage   82.75%   95.97%   +13.23%     
===========================================
  Files         344      351        +7     
  Lines       28515    29117      +602     
===========================================
+ Hits        23596    27945     +4349     
+ Misses       4919     1172     -3747     

Flag	Coverage Δ
unittests	95.97% <99.29%> (+13.23%)	⬆️

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

Impacted Files	Coverage Δ
src/Trixi.jl	71.43% <ø> (ø)
src/equations/equations.jl	97.87% <ø> (+4.26%)	⬆️
src/equations/shallow_water_two_layer_1d.jl	98.79% <98.79%> (ø)
src/equations/shallow_water_two_layer_2d.jl	99.38% <99.38%> (ø)
...1d_dgsem/elixir_shallowwater_twolayer_dam_break.jl	100.00% <100.00%> (ø)
...gsem/elixir_shallowwater_twolayer_well_balanced.jl	100.00% <100.00%> (ø)
...gsem/elixir_shallowwater_twolayer_well_balanced.jl	100.00% <100.00%> (ø)
...2d_dgsem/elixir_shallowwater_twolayer_dam_break.jl	100.00% <100.00%> (ø)
...gsem/elixir_shallowwater_twolayer_well_balanced.jl	100.00% <100.00%> (ø)

... and 93 files with indirect coverage changes

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