Entropy analysis and entropy stable DG methods for the Shallow Water Moment Equations

This reproducibility repository contains the information and code to reproduce the results of the article "Entropy analysis and entropy stable DG methods for the Shallow Water Moment Equations"

If you find these results useful, please cite the article mentioned above. If you use the implementations provided here, please also cite this repository as

@software{ersing2026swmeRepro,
  title={Reproducibility repository for "Entropy analysis and entropy stable {DG} methods for the {S}hallow {W}ater {M}oment {E}quations"},
  author={Julio Careaga, Patrick Ersing},
  year={2026},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.18460096},
  url          = {https://doi.org/10.5281/zenodo.18460096},
}

Installation

1. Install Julia v1.10
2. Download the repository

git clone git@github.com:patrickersing/paper-2025-swme-dg_dev.git

1. Set the working directory to the main folder and instantiate the Julia environment using

julia --project=. -e 'using Pkg; Pkg.instantiate()'

Usage

To reproduce the results in the paper start a new Julia session with the --project=. flag. It is possible (but optional) to use multiple threads by appending the --threads=N flag, to run on N threads.

julia --project=. --threads=N

Then execute the following commands in the Julia-REPL to create the respective results:

• Figure 1 The following command will create Figure 1 and save it as a .pdf

include("/figures/plot_figure_1.jl")

• Figure 2 The following command will create Figure 2 and save it as a .pdf

include("/figures/plot_figure_2.jl")

• Figure 3 The following command will create Figure 3 and save it as a .pdf

include("/figures/plot_figure_3.jl")

• Figure 4 & 5 The following command will create Figures 4 & 5 and and save them as a .pdf

include("/figures/plot_figure_4.jl")

• Table 1 & 2 The following command will print the convergence results for Table 1 to the Julia-REPL

using Trixi
convergence_test("/examples/elixir_shallowwater_moments_convergence.jl", 5)
convergence_test("/examples/elixir_shallowwater_linearized_moments_convergence.jl", 5)

Authors

• Patrick Ersing (Linköping University, Sweden)
• Julio Cesar Careaga Solis (University of Groningen, Netherlands)

Disclaimer

Everything is provided as is and without warranty. Use at your own risk!