留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Helbing流体力学交通流模型的守恒形式

李书峰 张鹏 黄仕进

李书峰, 张鹏, 黄仕进. Helbing流体力学交通流模型的守恒形式[J]. 应用数学和力学, 2011, 32(9): 1037-1045. doi: 10.3879/j.issn.1000-0887.2011.09.003
引用本文: 李书峰, 张鹏, 黄仕进. Helbing流体力学交通流模型的守恒形式[J]. 应用数学和力学, 2011, 32(9): 1037-1045. doi: 10.3879/j.issn.1000-0887.2011.09.003
LI Shu-feng, ZHANG Peng, Wong S C. Conservation Form of Helbing’s Fluid Dynamic Traffic Flow Model[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1037-1045. doi: 10.3879/j.issn.1000-0887.2011.09.003
Citation: LI Shu-feng, ZHANG Peng, Wong S C. Conservation Form of Helbing’s Fluid Dynamic Traffic Flow Model[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1037-1045. doi: 10.3879/j.issn.1000-0887.2011.09.003

Helbing流体力学交通流模型的守恒形式

doi: 10.3879/j.issn.1000-0887.2011.09.003
基金项目: 国家自然科学基金资助项目(11072141)
详细信息
    作者简介:

    李书峰(1981- ),男,河南洛阳人,硕士生(E-mail:shufengli1981@gmail.com);张鹏(1963- ),男,云南个旧人,教授,博士(联系人.E-mail:pzhang@mail.shu.edu.cn).

  • 中图分类号: TB126

Conservation Form of Helbing’s Fluid Dynamic Traffic Flow Model

  • 摘要: 得到了Helbing交通流流体力学模型的标准守恒形式,并证明了模型的双曲性,这对研究模型的解析性质和数值格式至关重要.基于给出的守恒形式,设计了高效求解模型方程的LDG(local discontinuous Galerkin)格式,并模拟了由不稳定平衡态到稳定的时停时走波的演化.数值模拟也表明,通过扩散系数校正确实使模型得到改进,避免了车辆碰撞和出现极端高密度.
  • [1] Lighthill M J, Whitham G B. On kinematic waves Ⅱ: a theory of traffic flow on long crowded roads[J].Proc Roy Soc A, 1995, 229(1178): 317-345.
    [2] Richards P I. Shock waves on the highway[J].Operations Research, 1956, 4(1): 42-51.
    [3] Payne H J. Models of freeway traffic and control[C]Bekey A G.Mathematical Models of Public Systems.Simulation Council Proc, La Jolla, 1971, 1: 51-61.
    [4] Whitham G B. Linear and Nonlinear Waves[M].New York: John Wiley and Sons, 1974.
    [5] Kerner B S, Konhuser P. Structure and parameters of clusters in traffic flow[J].Phys Rev E, 1994, 50(1): 54-83. doi: 10.1103/PhysRevE.50.54
    [6] Siebel F, Mauser W. On the fundamental diagram of traffic flow[J].SIAM J Appl Math, 2006, 66(4): 1150-1162. doi: 10.1137/050627113
    [7] Zhang P, Wong S C, Dai S Q. Characteristic parameters of a wide cluster in a higher-order traffic flow model[J].Chin Phys Lett, 2006, 23(2): 516-519. doi: 10.1088/0256-307X/23/2/067
    [8] Zhang P, Wong S C. Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models[J].Phys Rev E, 2006, 74(2): 026109. doi: 10.1103/PhysRevE.74.026109
    [9] Xu R Y, Zhang P, Dai S Q, Wong S C. Admissibility of a wide cluster solution in anisotropic higher-order traffic flow models.[J].SIAM J Appl Math, 2007, 68(2): 562-573. doi: 10.1137/06066641X
    [10] Zhang P, Wong S C, Dai S Q. A conserved higher-order anisotropic traffic flow model: description of equilibrium and non-equilibrium flows[J].Transpn Res Part B, 2009, 43(5): 562-574. doi: 10.1016/j.trb.2008.10.001
    [11] Tang T Q, Huang H J, Shang H Y. A new macro model for traffic flow with the consideration of the driver’s forecast effect[J].Physics Letters A, 2010, 374(15/16): 1668-1672. doi: 10.1016/j.physleta.2010.02.001
    [12] Prigogine I, Herman R. Kinetic Theory of Vehicular Traffic[M].New York: American Elsevier Publishing Co,1971.
    [13] Paveri-Fontana S L. On Boltzmann-like treatments for traffic flow: a critical review of the basic model and an alternative proposal for dilute traffic analysis[J].Transpn Res, 1975, 9(4): 225-235. doi: 10.1016/0041-1647(75)90063-5
    [14] Phillips W. Kinetic Model for Traffic Flow[M].Springfield, VA: National Technical Information Service, 1977.
    [15] Helbing D. A fluid-dynamic model for the movement of pedestrians[J].Complex Systems, 1992, 6(5): 391-415.
    [16] Helbing D, Hennecke A, Shvetsov V, Treiber M. Master: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model[J]. Transpn Res Part B, 2001, 35(2): 183-211. doi: 10.1016/S0191-2615(99)00047-8
    [17] Hoogendoorn S P, Bovy P H L. Continuum modeling of multiclass traffic flow[J]. Transpn Res Part B, 2000, 34(2): 123-146. doi: 10.1016/S0191-2615(99)00017-X
    [18] Hoogendoorn S P, Bovy P H L. Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow[J]. Transpn Res Part B, 2001, 35(4): 317-336. doi: 10.1016/S0191-2615(99)00053-3
    [19] Ngoduy D. Derivation of continuum traffic model for weaving sections on freeways[J]. Transportmetrica, 2006, 2(3): 199-222. doi: 10.1080/18128600608685662
    [20] Ngoduy D. Application of gas-kinetic theory to modeling mixed traffic of manual and ACC vehicles[J]. Transportmetrica, doi: 10.1080/18128600903578843.
    [21] Helbing D. Improved fluid-dynamic model for vehicular traffic[J].Phys Rev E, 1995, 51(4): 3164-3169.
    [22] Liu T P. Hyperbolic and viscous conservation laws[C]CBMS-NSF Regional Conference Series in Applied Mathematics 72, SIAM, Philadelphia, PA, 2000.
    [23] Cockburn B, Lin S Y, Shu C W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws Ⅲ: one dimensional systems[J].J Comput Phys, 1989, 84(1): 90-113. doi: 10.1016/0021-9991(89)90183-6
    [24] Cockburn B, Shu C W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems[J].SIAM J Numer Anal, 1998, 35(6): 2440-2463. doi: 10.1137/S0036142997316712
    [25] Bassi F, Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations[J].J Comput Phys, 1997, 131(2): 267-279. doi: 10.1006/jcph.1996.5572
  • 加载中
计量
  • 文章访问数:  1512
  • HTML全文浏览量:  117
  • PDF下载量:  893
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-03-23
  • 修回日期:  2011-06-20
  • 刊出日期:  2011-09-15

目录

    /

    返回文章
    返回