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Mathematics > Numerical Analysis

arXiv:2209.05137 (math)
[Submitted on 12 Sep 2022]

Title:Central schemes for networked scalar conservation laws

Authors: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.
Comments: 29 pages, 8 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M08, 35R02, 35L02
Cite as: arXiv:2209.05137 [math.NA]
  (or arXiv:2209.05137v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2209.05137

Submission history

From: Niklas Kolbe [view email]
[v1] Mon, 12 Sep 2022 10:45:12 UTC (166 KB)
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