TL;DR
This paper introduces a new numerical scheme for scalar conservation laws on networks that avoids solving Riemann problems at junctions, using relaxation systems to ensure mass conservation and ease of computation.
Contribution
The authors develop a relaxation-based scheme for networked scalar conservation laws that simplifies coupling conditions and extends to higher order, applicable to traffic and two-phase flow models.
Findings
Scheme is mass conservative and easy to implement.
Provides well-defined coupling conditions for complex networks.
Demonstrates effectiveness in traffic flow simulations.
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.
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