Central schemes for networked scalar conservation laws
Numerical Analysis
2022-09-13 v1 Numerical Analysis
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
Cite
@article{arxiv.2209.05137,
title = {Central schemes for networked scalar conservation laws},
author = {Michael Herty and Niklas Kolbe and Siegfried Müller},
journal= {arXiv preprint arXiv:2209.05137},
year = {2022}
}
Comments
29 pages, 8 figures