Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks

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 solv...

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Bibliographic Details
Published inCommunications on Applied Mathematics and Computation (Online) Vol. 4; no. 3; pp. 986 - 1010
Main Authors Vacek, Lukáš, Kučera, Václav
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.09.2022
Subjects
Applications of Mathematics
Computational Science and Engineering
Mathematics
Mathematics and Statistics
Original Paper
Discontinuous Galerkin method
Traffic flow
Conservations laws on networks
Numerical flux
35L04
65M60
76A30
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Summary: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.
ISSN:2096-6385
2661-8893
DOI:10.1007/s42967-021-00169-8