532 | RWTH Publication No: 854171 2022   |
TITLE | Central schemes for networked scalar conservation laws |
AUTHORS | Michael Herty, Niklas Kolbe, Siegfried Müller |
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. |
KEYWORDS | Coupled conservation laws, finite-volume schemes, coupling conditions |
DOI | 10.3934/nhm.2023012 |
PUBLICATION | Networks and heterogeneous media 18(1), pp. 310-340 |