2022/04/10 by Jan Friedrich, Friedrich, Jan, Simone Göttlich +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #35L65 #65M12 #76A30 #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Traffic control and management
paper · pdf · doi:10.48550/arxiv.2204.04640
openalex publication_date 2022/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.