Helbing流体力学交通流模型的守恒形式  

Conservation Form of Helbing's Fluid Dynamic Traffic Flow Model

作　　者：李书峰[1,2] 张鹏[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]上海大学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》2011年第9期1037-1045,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(11072141)

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(lo-cal 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.A standard conservation form was derived, the hyperbolicity of Helbing＇ s fluid dy nalnic traffic flow model was proved, which was essential for general analytical and numerical study of this model. On the basis of this conservation form, a local discontinuous Galerldn scheme is designed to solve the resulting model efficiently. The evolution of an unstable equilib- rium traffic state leading to a stable stop-and-go traveling wave was simulated. This simulation also verifies that the model has been truly improved through the introduction of modified diffusion coefficients, thereby helping to protect vehicles from collisions and avoiding the appearance of extremely large density.

关 键 词：守恒形式 双曲性 LDG格式 时走时停波 

分 类 号：TB126[理学—工程力学]