Bound-preserving limiting for Runge-Kutta methods

This repository contains the code to reproduce the results in "Bound-preserving convex limiting for high-order Runge-Kutta time discretizations of hyperbolic conservation laws" by D. Kuzmin, M. Quezada de Luna, D.I. Ketcheson and J. Grull.

Dependencies

This code requires Python 3 (we use 3.7.7) and the following libraries:

numpy

matplotlib

scipy

nodepy

A fortran compiler

f2py

Compilation

Inside the folder 'code', type make.

Running the examples

The code run_problems.py calls functions inside time_flux_limiting.py to run the different problems in the manuscript. Inside run_problems.py there are different 'sections' that can be activated via if False/True statements. Activate the different sections to create the different tables and figures in the manuscript. The following sections are inside run_convergence.py:

CONVERGENCE OF SEMI-DISCRETIZATION. This code produces the results in Section 5.1.

CONVERGENCE TO SMOOTH SOLUTIONS. If solution_type=0, the code produces the results in the first part of Section 5.2. If solution_type=3, the code produces the results in the first part of Section 5.3.

LINEAR ADVECTION WITH NON-SMOOTH SOLUTION. This code produces the results in the second part of Section 5.2.

NONLINEAR BURGERS AFTER SHOCK. This code produces the results in the second part of Section 5.3.

NONLINEAR ONE DIM KPP. This code produces the results in Section 5.4.