交通流流体力学模型与非线性波  

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

作　　者：张鹏[1,2] 王卓[1,2] 黄仕进[3] 

机构地区：[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

出　　处：《应用数学和力学》2013年第1期85-97,共13页Applied Mathematics and Mechanics

基　　金：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)

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.Fluid dynamics methods were used in modeling traffic flow problems, which demon- strated many interesting non-linear propagation phenomena. It was summarized that the propa- gation was related to traffic pressures and serf-driven forces, which generated shock and rare- faction 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 Riemarm problem arising from extension of the LWR model to traffic networks was also introduced in detail. And a system based on the Navi- er-Stokes equations was proposed to model the 2-dimensional pedestrian flow problem with ap- plication of the Eikon equation for determination of a pedestrian＇ s desired motion direction.

关 键 词：守恒律方程 激波 时走时停波 超车波 接触间断 

分 类 号：O29[理学—应用数学]