Code that implements the schemes of the two papers
Central schemes for networked scalar conservation laws
and
A Central Scheme for Two Coupled Hyperbolic Systems
by M. Herty, N. Kolbe, S. Müller
The first paper is published open access in Networks and Heterogeneous Media. The second paper is accepted in Communications on Applied Mathematics and Computation.
Julia codes were written by N. Kolbe
The repository contains a Julia project environment, which includes the package CentralNetworkScheme.jl implementating the schemes, and a directory (experiments) with scripts for various numerical experiments. The former implements schemes for 1-to-1 and 2-to-1 networks. Flux functions and boundary conditions can be freely chosen. Users can either use the first or the second order central scheme. For the LWR model on 2-to-1 networks the central coupling approach can be replaced by the flow maximization approach.
Experiments on 1-to-1 networks for the Burgers' equation (experiments/Burgers11.jl) and on 2-to-1 networks for the LWR model (experiments/LWR21.jl) and the Buckley-Leverett equation (experiments/BL21) are included in the experiments folder.
Clone the repository on your local machine. To run the scripts activate the project environment, for example, by starting julia from the command line within the root folder of the repository, then changing to pkg mode typing ] and afterwards running activate .. Then the experiments can be run by including the corresponding scripts, e.g., include("experiments/LWR21.jl"). You can get started by going through the scripts and modifying them as you like. Scripts are commented and further documentation will be added in the future.
In case of questions or problems please contact the authors of the paper or file a GitHub issue in this repository.