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

多等级交通流LWR模型中的非线性波描述与WENO数值逼近

张鹏 戴世强 刘儒勋

张鹏, 戴世强, 刘儒勋. 多等级交通流LWR模型中的非线性波描述与WENO数值逼近[J]. 应用数学和力学, 2005, 26(6): 637-644.
引用本文: 张鹏, 戴世强, 刘儒勋. 多等级交通流LWR模型中的非线性波描述与WENO数值逼近[J]. 应用数学和力学, 2005, 26(6): 637-644.
ZHANG Peng, DAI Shi-qiang, LIU Ru-xun. Description and WENO Numerical Approximation to Nonlinear Waves of a Multi-Class Traffic Flow LWR Model[J]. Applied Mathematics and Mechanics, 2005, 26(6): 637-644.
Citation: ZHANG Peng, DAI Shi-qiang, LIU Ru-xun. Description and WENO Numerical Approximation to Nonlinear Waves of a Multi-Class Traffic Flow LWR Model[J]. Applied Mathematics and Mechanics, 2005, 26(6): 637-644.

多等级交通流LWR模型中的非线性波描述与WENO数值逼近

基金项目: 国家自然科学基金资助项目(10472064;10371118);中国博士后科学基金资助项目(2003034254);国家教育部博士点专项基金资助项目(20040280014)
详细信息
    作者简介:

    张鹏(1963- ),男,云南个旧人,副教授,博士(联系人.Tel:+86-21-56331458;Fax:+86-21-36033087;E-mail:pengzhang@ustc.edu.cn).

  • 中图分类号: TB126

Description and WENO Numerical Approximation to Nonlinear Waves of a Multi-Class Traffic Flow LWR Model

  • 摘要: 证明了交通流多等级LWR(Lighthill-Whitham-Richards)模型的双曲性质,并根据交通流的特征给出关于其非线性波的描述,主要包括车流通过激波和稀疏波时密度和速度的单调性变化.由于方程组没有显式的特征分解,所以引入具有高分辨和高精度的WENO(weighted essentially non~oscillatory)格式作数值模拟,得到与理论描述完全一致的数值结果.
  • [1] 戴世强,冯苏苇,顾国庆.交通流动力学:它的内容、方法和意义[J].自然杂志,1997,11(4):196—201.
    [2] Helbing D.Traffic and related self-driven many-particle systems[J].Rev Mod Phys,2001,73(4):1067—1141. doi: 10.1103/RevModPhys.73.1067
    [3] Lighthill M H,Whitham G B.On kinematics wave—Ⅱ a theory of traffic flow on long crowded roads[J].Proc Roy Soc London,Ser A,1955,22:317—345.
    [4] Richards P I.Shack waves on the highway[J].Operations Research,1956,4(2):42—51. doi: 10.1287/opre.4.1.42
    [5] Wong G C K,Wong S C.a multi-class traffic flow model—an extension of LWR model with heterogeneous drivers[J].Transpn Res A,2002,36(9):827—841.
    [6] Harten A,Engquish B,Osher S,et al.Uniformly high order essentially non-oscillatory schemes Ⅲ[J].J Comput Phys,1987,71(2):231—303. doi: 10.1016/0021-9991(87)90031-3
    [7] Jiang G,Shu C -W.Efficient implementation of weighted ENO schemes[J].J Comput Phys,1996,126(1):202—228. doi: 10.1006/jcph.1996.0130
    [8] Liu X -D,Osher S,Chan T.Weighted essentially nonoscillatory schemes[J].J Comput Phys,1994,115(1):200—212. doi: 10.1006/jcph.1994.1187
    [9] Shu C -W.Lecture Notes in Mathematics-Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws[R]. 1697, Cetraro, Italy: Springe, 1997,329—432.
    [10] Whitham G B.Linear and Nonlinear Waves[M].NY: John Wiley and Sons, 1974.
    [11] Lax P D.Shock Waves and Entropy.In:Zarantonello E A Ed.Nonlinear Functional Analysis[M].New York:Academic Press, 1971.
    [12] Lax P D.Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves[M].Philadelphia:SIAM,1973.
    [13] Toro E F.Riemann Solvers and Numerical Methods for Fluid Dynamics[M].Berlin:Springer~Verlay,1999.
    [14] Shu C -W.TVB uniformly high order scheme for conservation laws[J].Mathematics of Computation,1987,49(179):105—121. doi: 10.1090/S0025-5718-1987-0890256-5
    [15] Shu C -W.Total-variation-diminishing time discretizations[J].SIAM Journal on Scientific and Statistical Computation,1988,9(4):1073—1084. doi: 10.1137/0909073
  • 加载中
计量
  • 文章访问数:  2554
  • HTML全文浏览量:  136
  • PDF下载量:  634
  • 被引次数: 0
出版历程
  • 收稿日期:  2003-12-30
  • 修回日期:  2005-02-05
  • 刊出日期:  2005-06-15

目录

    /

    返回文章
    返回