交通流流体力学模型与非线性波

张鹏; 王卓; 黄仕进

doi:10.3879/j.issn.1000-0887.2013.01.009

交通流流体力学模型与非线性波

doi: 10.3879/j.issn.1000-0887.2013.01.009

张鹏^1,2,
王卓^1,2,
黄仕进³

¹上海大学上海市应用数学和力学研究所,上海 200072;²上海市力学在工程中的应用重点实验室,上海 200072;³香港大学土木工程系,香港

基金项目: 国家自然科学基金资助项目(11072141;11272199);国家重点基础研究发展计划资助项目(2012CB725404);上海市重点学科建设资助项目(S30106)

详细信息

作者简介:
张鹏 (1963—),男,云南个旧人,教授(通讯作者.E-mail: pzhang@mail.shu.edu.cn).

中图分类号: O29
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- 被引次数: 0
出版历程
- 收稿日期: 2012-11-19
- 修回日期: 2012-12-10
- 刊出日期: 2013-01-15

Fluid Dynamics Traffic Flow Models and Their Related Non-Linear Waves

¹Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai 200072, P.R.China;²Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai 200072, P.R.China;³Department of Civil Engineering,The University of Hong Kong, Pokfulam Road,Hong Kong SAR, P.R.China

摘要

摘要: 介绍了交通流问题中的流体力学描述方法，分析了交通流在受压力和自驱动力等因素作用下所产生的非线性波动现象．这些描述包括LWR运动学模型，考虑动力学效应的高阶模型，考虑超车效应的多车种LWR(Lighthill-Whitham-Richards)模型，以及考虑流通量间断的模型方程．此外，还介绍了LWR网络推广模型在交叉口的Riemann问题求解；提出了描述二维行人流问题的Navier-Stokes-Eikon方程模型并描述了确定行人流运动期盼方向的基本思想．
- 守恒律方程 /
- 激波 /
- 时走时停波 /
- 超车波 /
- 接触间断
Abstract: Fluid dynamics methods were used in modeling traffic flow problems, which demonstrated many interesting nonlinear propagation phenomena. It was summarized that the propagation was related to traffic pressures and self-driven forces, which generated shock and rarefaction waves in the LWR model, stop-and-go waves in the higher-order model, overtaking waves (shock or rarefaction waves) in the multi-class LWR model, and a contact discontinuity in problems with discontinuous fluxes. The Riemann problem arising from extension of the LWR model to traffic networks was also introduced in detail. And a system based on the Navier-Stokes equations was proposed to model the 2-dimensional pedestrian flow problem with application of the Eikon equation for determination of a pedestrian’s desired motion direction.
- conservation laws /
- shock /
- stop-and-go wave /
- overtaking wave /
- contact discontinuity

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