Conservation laws with discontinuous flux function on networks: a splitting algorithm. (English) Zbl 1532.90021
Summary: In this article, we present an extension of the splitting algorithm proposed in [J. D. Towers, J. Comput. Phys. 421, Article ID 109722, 30 p. (2020; Zbl 1537.76009)] 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.
MSC:
| 90B10 | Deterministic network models in operations research |
| 90B20 | Traffic problems in operations research |
| 35L65 | Hyperbolic conservation laws |
Keywords:
traffic flow networks; LWR model; conservation laws with discontinuous flux; numerical schemes; splitting algorithmCitations:
Zbl 1537.76009References:
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