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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (4): 523-528.doi: https://doi.org/10.1007/s10483-013-1687-9

• • 上一篇    

Solitary wave solution to Aw-Rascle viscous model of traffic flow

吴春秀1,2 张鹏1 S. C. WONG3 乔殿梁1 戴世强1   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. College of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, Fujian Province, P. R. China;
    3. Department of Civil Engineering, The University of Hong Kong, Hong Kong, P. R. China
  • 出版日期:2013-04-03 发布日期:2013-04-03
  • 通讯作者: Peng ZHANG E-mail:pzhang@mail.shu.edu.cn

Solitary wave solution to Aw-Rascle viscous model of traffic flow

Chun-xiu Wu1,2, Peng ZHANG1, S. C. WONG3, Dian-liang QIAO1, Shi-xiang DAI1   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. College of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, Fujian Province, P. R. China;
    3. Department of Civil Engineering, The University of Hong Kong, Hong Kong, P. R. China
  • Online:2013-04-03 Published:2013-04-03
  • Contact: Peng ZHANG E-mail:pzhang@mail.shu.edu.cn

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636

被引次数

7

摘要： A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.

关键词: linear periodic system; parameter uncertainty;robust stability;linear matrix inequality (LMI);state feedback;stabilization;$\mathcal{L}_2$-gain, higher-order traffic flow model, hyperbolic conservation law, traveling wave solution, conservative scheme

Abstract: A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.

Key words: linear periodic system; parameter uncertainty;robust stability;linear matrix inequality (LMI);state feedback;stabilization;$\mathcal{L}_2$-gain, conservative scheme, hyperbolic conservation law, higher-order traffic flow model, traveling wave solution

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