Conservation form of Helbing's fluid dynamic traffic flow model  

作　　者：李书峰 张鹏 S.C.WONG 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University [2]Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai University [3]Department of Civil Engineering,The University of Hong Kong

出　　处：《Applied Mathematics and Mechanics(English Edition)》2011年第9期1109-1118,共10页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 11072141);the Shanghai Program for Innovative Research Team in Universities;the University Research Committee of the University of Hong Kong (No. 201007176059);the Outstanding Researcher Award from the University of Hong Kong

摘　　要：A standard conservation form is derived in this paper.The hyperbolicity of Helbing＇s fluid dynamic traffic flow model is proved,which is essential to the general analytical and numerical study of this model.On the basis of this conservation form,a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently.The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated.This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients,and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.A standard conservation form is derived in this paper.The hyperbolicity of Helbing＇s fluid dynamic traffic flow model is proved,which is essential to the general analytical and numerical study of this model.On the basis of this conservation form,a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently.The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated.This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients,and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.

关 键 词：conservation form HYPERBOLICITY local discontinuous Galerkin method stop-and-go wave 

分 类 号：U491.112[交通运输工程—交通运输规划与管理] O351.2[交通运输工程—道路与铁道工程]