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Description and weno numerical approximation to nonlinear waves of a multi-class traffic flow LWR model

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Abstract

A strict proof of the hyperbolicity of the multi-class LWR (Lighthill-Whitham-Richards) traffic flow model, as well as the descriptions on those nonlinear waves characterized in the traffic flow problems were given. They were mainly about the monotonicity of densities across shocks and in rarefactions. As the system had no characteristic decomposition explicitly, a high resolution and higher order accuracy WENO (weighted essentially non-oscillatory) scheme was introduced to the numerical simulation, which coincides with the analytical description.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, P. R. China

    Zhang Peng (Associate Professor, Doctor) & Dai Shi-qiang

  2. Department of Mathematics, University of Science & Technology of China, 230026, Hefei, P. R. China

    Zhang Peng (Associate Professor, Doctor) & Liu Ru-xun

Authors
  1. Zhang Peng
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  2. Dai Shi-qiang
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  3. Liu Ru-xun
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Corresponding author

Correspondence to Zhang Peng.

Additional information

Contributed by DAI Shi-qiang

Project supported by the National Natural Science Foundation of China (Nos. 10472064, 10371118); the Post-Doctoral Science Foundation of China (No. 2003034254) and the Special Fund for PhD Program of Education Ministry of China (No. 20040280014)

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Peng, Z., Shi-qiang, D. & Ru-xun, L. Description and weno numerical approximation to nonlinear waves of a multi-class traffic flow LWR model. Appl Math Mech 26, 691–699 (2005). https://doi.org/10.1007/BF02465418

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  • DOI: https://doi.org/10.1007/BF02465418

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

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