639 RWTH Publication No: 981041        2022       
TITLE Conservation laws with discontinuous flux function on networks: a splitting algorithm
AUTHORS Jan Friedrich, Simone Göttlich, Annika Uphoff
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.
KEYWORDS Traffic flow networks, conservation laws with discontinuous flux, numerical schemes
DOI 10.3934/nhm.2023001