Central schemes for networked scalar conservation laws

arXiv (Cornell University)

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(3), 235-276 (1995)] 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 Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

2. Niklas Kolbe Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

3. Siegfried Müller Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen