Central schemes for networked scalar conservation laws

Abstract

<abstract><p>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, <italic>Comm. Pure. Appl. Math.</italic> <bold>48</bold> (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.</p></abstract>