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Add Roe dissipation for SWE #73

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This PR adds a Roe dissipation term for the ShallowWaterEquationsWetDry1D and ShallowWaterEquationsWetDry2D. The dissipation term can be combined using FlusPlusDissipation(flux_central, dissipation_roe) to obtain the classical Roe flux.

@patrickersing patrickersing added the enhancement New feature or request label Mar 7, 2025
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codecov bot commented Mar 7, 2025

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.30%. Comparing base (ac44c0b) to head (365cd90).

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@@            Coverage Diff             @@
##             main      #73      +/-   ##
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+ Coverage   99.28%   99.30%   +0.01%     
==========================================
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  Lines        2652     2716      +64     
==========================================
+ Hits         2633     2697      +64     
  Misses         19       19              

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Convergence results for "../examples/tree_1d_dgsem/elixir_shallowwater_source_terms.jl" with polydeg = 3, surface_flux = (FluxPlusDissipation(flux_central, dissipation_roe), flux_nonconservative_fjordholm_etal):

Screenshot from 2025-03-07 11-41-37

Convergence results for "../examples/tree_2d_dgsem/elixir_shallowwater_source_terms.jl" with polydeg = 3, surface_flux = (FluxPlusDissipation(flux_central, dissipation_roe), flux_nonconservative_fjordholm_etal):

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Overall, the new dissipation terms look good. I added some references to the docstrings.

dissipation_roe(u_ll, u_rr, orientation_or_normal_direction,
equations::ShallowWaterEquationsWetDry1D)
Roe-type dissipation term for the [`ShallowWaterEquationsWetDry1D`](@ref). To create the classical Roe solver,
this dissipation term can be combined with [`Trixi.flux_central`](@extref) using [`Trixi.FluxPlusDissipation`](@extref).
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Suggested change
this dissipation term can be combined with [`Trixi.flux_central`](@extref) using [`Trixi.FluxPlusDissipation`](@extref).
this dissipation term can be combined with [`Trixi.flux_central`](@extref) using [`Trixi.FluxPlusDissipation`](@extref).
For details on the Roe linearization see Chapter 15.3.2 and Chapter 15.3.3 for the one-dimensional
shallow water equations of the book:
- Randall J. LeVeque (2002)
Finite Volume Methods for Hyperbolic Problems
[DOI: 10.1017/CBO9780511791253](https://doi.org/10.1017/CBO9780511791253)

dissipation_roe(u_ll, u_rr, orientation_or_normal_direction,
equations::ShallowWaterEquationsWetDry2D)
Roe-type dissipation term for the [`ShallowWaterEquationsWetDry2D`](@ref). To create the classical Roe solver,
this dissipation term can be combined with [`Trixi.flux_central`](@extref) using [`Trixi.FluxPlusDissipation`](@extref).
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Suggested change
this dissipation term can be combined with [`Trixi.flux_central`](@extref) using [`Trixi.FluxPlusDissipation`](@extref).
this dissipation term can be combined with [`Trixi.flux_central`](@extref) using [`Trixi.FluxPlusDissipation`](@extref).
For details on the Roe linearization see Chapter 15.3.2 and Chapter 21.7 for the two-dimensional
shallow water equations of the book:
- Randall J. LeVeque (2002)
Finite Volume Methods for Hyperbolic Problems
[DOI: 10.1017/CBO9780511791253](https://doi.org/10.1017/CBO9780511791253)

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