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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (9): 1109-1118.doi: https://doi.org/10.1007/s10483-011-1485-9

• Articles • 上一篇    下一篇

Conservation form of Helbing’s fluid dynamic traffic flow model

李书峰1,2 张鹏1,2 S.C.WONG3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China;
    3. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, P. R. China
  • 收稿日期:2011-03-23 修回日期:2011-06-23 出版日期:2011-09-02 发布日期:2011-09-02

Conservation form of Helbing’s fluid dynamic traffic flow model

 LI Shu-Feng1,2, ZHANG Peng1,2, S.C.WONG3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China;
    3. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, P. R. China
  • Received:2011-03-23 Revised:2011-06-23 Online:2011-09-02 Published:2011-09-02

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摘要： A standard conservation form is derived in this paper. The hyperbolicity of Helbing’s fluid dynamic traffic flow model is proved, which is essential to the general analytical and numerical study of this model. On the basis of this conservation form, a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently. The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated. This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients, and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.

Abstract: A standard conservation form is derived in this paper. The hyperbolicity of Helbing’s fluid dynamic traffic flow model is proved, which is essential to the general analytical and numerical study of this model. On the basis of this conservation form, a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently. The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated. This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients, and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.

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