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Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks

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Abstract

In this paper, we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters. To solve traffic flows on networks, we construct suitable numerical fluxes at junctions based on preferences of the drivers. We prove basic properties of the constructed numerical flux and the resulting scheme and present numerical experiments, including a junction with complicated traffic light patterns with multiple phases. Differences with the approach to numerical fluxes at junctions from Čanić et al. (J Sci Comput 63: 233–255, 2015) are discussed and demonstrated numerically on a simple network.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Sokolovská 49/83, 186 00, Prague, Czech Republic

    Lukáš Vacek & Václav Kučera

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  1. Lukáš Vacek
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  2. Václav Kučera
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Correspondence to Lukáš Vacek.

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The authors declare that they have no conflict of interest.

Additional information

The work of L. Vacek is supported by the Charles University, project GA UK No. 1114119. The work of V. Kučera is supported by the Czech Science Foundation, project No. 20-01074S.

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Vacek, L., Kučera, V. Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks. Commun. Appl. Math. Comput. 4, 986–1010 (2022). https://doi.org/10.1007/s42967-021-00169-8

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  • DOI: https://doi.org/10.1007/s42967-021-00169-8

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