4.5 Article

A relaxation scheme for a multi-class Lighthill-Whitham-Richards traffic flow model

Journal

JOURNAL OF ZHEJIANG UNIVERSITY-SCIENCE A
Volume 10, Issue 12, Pages 1835-1844

Publisher

ZHEJIANG UNIV
DOI: 10.1631/jzus.A0820829

Keywords

Relaxation scheme; Multi-class LWR model; Traffic flow; CWENO reconstruction; Implicit-explicit Runge-Kutta

Funding

  1. Aoxiang Project and the Scientific and Technological Innovation Foundation of Northwestern Polytechnical University, China [2007KJ01011]

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We present a high-resolution relaxation scheme for a multi-class Lighthill-Whitham-Richards (MCLWR) traffic flow model. This scheme is based on high-order reconstruction for spatial discretization and an implicit-explicit Runge-Kutta method for time integration. The resulting method retains the simplicity of the relaxation schemes. There is no need to involve Riemann solvers and characteristic decomposition. Even the computation of the eigenvalues is not required. This makes the scheme particularly well suited for the MCLWR model in which the analytical expressions of the eigenvalues are difficult to obtain for more than four classes of road users. The numerical results illustrate the effectiveness of the presented method.

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