Skip to content

Central schemes for networks of scalar conservation laws

License

Notifications You must be signed in to change notification settings

nklb/CentralNetworkScheme

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

16 Commits
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

Implementation of central schemes for networks of scalar conservation laws

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

Contents

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.

Usage

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.

About

Central schemes for networks of scalar conservation laws

Topics

Resources

License

Stars

Watchers

Forks

Releases

No releases published

Packages

No packages published

Languages