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