Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks

doi:10.1007/s42967-021-00169-8

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (3): 986-1010.doi: 10.1007/s42967-021-00169-8

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Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks

Lukáš Vacek, Václav Kučera

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

收稿日期:2020-08-24 修回日期:2021-09-02 出版日期:2022-09-20 发布日期:2022-07-04
通讯作者: Lukáš Vacek,E-mail:lvacek@karlin.mff.cuni.cz;Václav Kučera,E-mail:kucera@karlin.mff.cuni.cz E-mail:lvacek@karlin.mff.cuni.cz;kucera@karlin.mff.cuni.cz
基金资助:
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.

Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks

Lukáš Vacek, Václav Kučera

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

Received:2020-08-24 Revised:2021-09-02 Online:2022-09-20 Published:2022-07-04
Contact: Lukáš Vacek,E-mail:lvacek@karlin.mff.cuni.cz;Václav Kučera,E-mail:kucera@karlin.mff.cuni.cz E-mail:lvacek@karlin.mff.cuni.cz;kucera@karlin.mff.cuni.cz
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: Traffic flow, Conservations laws on networks, Discontinuous Galerkin method, Numerical flux

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.

Key words: Traffic flow, Conservations laws on networks, Discontinuous Galerkin method, Numerical flux

中图分类号:

Lukáš Vacek, Václav Kučera. Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks[J]. Communications on Applied Mathematics and Computation, 2022, 4(3): 986-1010.

参考文献

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Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks

Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks

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