Overview

This repository contains the code for the paper titled information geometric regularization of the barotropic Euler equations.

Instantiating packages

To run the experiments for the 1d or 2d problems, enter the folders IGR1D1 or IGR2D and type

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

You can now reproduce the experiments as follows:

1D Problems

The csv files for Figures 11 and 12 in the current draft can be generated by running

julia --project=. plot_1d_sine.jl
julia --project=. plot_shu_osher.jl

The csv files for the convergence study in Figure 13 are generated by running

julia --project=. convergence_shock.jl
julia --project=. convergence_smooth.jl

Finally, the comparison to localized artificial diffusivity in Figure 20 is run by

julia --project=. LAD_comparison_dissipation.jl
julia --project=. LAD_comparison_oscillation.jl

2D Problems

Numerical results for the blast wave problem are run by

julia --project=. blast_waves.jl

and those of the two colliding shock waves are run by

julia --project=. two_sines_x.jl

These routines save the result as JLD files in out/jlsrl, with a file name that reflects the parameter choices.

Figures like Figures 15, 17-19 can then be produced by running

julia --project=. plot_alpha_convergence_two_sines.jl
julia --project=. plot_densities_blast_waves.jl
julia --project=. plot_densities_two_sines.jl
julia --project=. plot_longterm_densities_two_sines.jl
julia --project=. plot_mesh_convergence_two_sines.jl

The csv files for Figure 16 are obtained (from the corresponding JLD file) by running

julia --project=. plot_mesh_convergence_two_sines.jl