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

Networks and Heterogeneous Media, vol. 18, pp. 1–28

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.

Authors 3

1. Jan O. Friedrich Aachen Institute of Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Applied Mathematics, 52064 Aachen, Germany

2. Simone Göttlich

   University of Mannheim

   Affiliation as printed

   University of Mannheim, Department of Mathematics, 68131 Mannheim, Germany

3. Annika Uphoff corresponding Aachen Institute of Applied Mathematics

   RWTH Aachen University · University of Mannheim

   Affiliation as printed

   University of Mannheim, Department of Mathematics, 68131 Mannheim, Germany

   RWTH Aachen University, Institute of Applied Mathematics, 52064 Aachen, Germany