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Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.12 P.1835~1844

10.1631/jzus.A0820829


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


Author(s):  Jian-zhong CHEN, Zhong-ke SHI, Yan-mei HU

Affiliation(s):  College of Automation, Northwestern Polytechnical University, Xi’ more

Corresponding email(s):   jzhchen@nwpu.edu.cn

Key Words:  Relaxation scheme, Multi-class LWR model, Traffic flow, CWENO reconstruction, Implicit-explicit Runge-Kutta


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Jian-zhong CHEN, Zhong-ke SHI, Yan-mei HU. A relaxation scheme for a multi-class Lighthill-Whitham-Richards traffic flow model[J]. Journal of Zhejiang University Science A, 2009, 10(12): 1835~1844.

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Abstract: 
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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