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arXiv · 2209.05137

Central schemes for networked scalar conservation laws

Michael Herty·Niklas Kolbe·Siegfried Müller
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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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Michael Herty, Niklas Kolbe, Siegfried Müller. 2022-09-12. Central schemes for networked scalar conservation laws. https://arxiv.org/abs/2209.05137

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