Central schemes for networked scalar conservation laws

Networks and Heterogeneous Media, vol. 18, pp. 310–340

Abstract

We propose a novel scheme to numerically solve scalar conservation laws on networks without the necessity to solve Riemann problems at the junction. The scheme is derived using the relaxation system introduced in [Jin and Xin, Comm. Pure. Appl. Math. 48 (1995), 235-276] and taking the relaxation limit also at the nodes of the network. The scheme is mass conservative and yields well defined and easy-to-compute coupling conditions even for general networks. We discuss higher order extension of the scheme and applications to traffic flow and two-phase flow. In the former we compare with results obtained in literature.

Authors 3

1. Michaël Herty
2. Niklas Kolbe
3. Siegfried Müller corresponding Aachen Institute of Geometry and Practical Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute of Geometry and Practical Mathematics, RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany