@article{Herty2023, 
author = {Michael Herty and Niklas Kolbe and Siegfried Müller},
title = {Central schemes for networked scalar conservation laws},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {1},
pages = {310-340},
keywords = {Coupled conservation laws, finite-volume schemes, coupling conditions, relaxation system, scalar conservation laws},
url = {https://www.sciopen.com/article/10.3934/nhm.2023012},
doi = {10.3934/nhm.2023012},
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 (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.}
}