流通量间断守恒高阶交通流模型及其数值模拟  

A Conserved High-Order Traffic Flow Model With Discontinuous Flux and Its Numerical Simulation

作　　者：乔殿梁[1] 李晓洋 郭明旻 张鹏[1,3] QIAO Dianliang;LI Xiaoyang;GUO Mingmin;ZHANG Peng(Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai 200072, P.R.China;Department of Aeronautics and Astronautics,Fudan University,Shanghai 200433, P.R.China;Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai 200072, P.R.China)

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]复旦大学航空航天系,上海200433 [3]上海市力学在能源工程中的应用重点实验室,上海200072

出　　处：《应用数学和力学》2019年第5期546-561,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(面上项目)(11672348;11272199);国家重点研发计划(2018YFB1600900);国家重点基础研究发展计划(973计划)(2012CB725404)~~

摘　　要：在非均匀道路条件下,推广了各向异性守恒高阶交通流模型(CHO模型),获得流通量间断CHO模型,并基于其Riemann不变量性质,运用局部简化方法及δ映射算法,设计了求解流通量间断CHO模型的一阶Godunov、EO(Engquist-Osher)和LF(Lax-Friedrichs)等数值格式.通过数值模拟表明流通量间断CHO模型是合理有效的,它可以描述平衡态和非平衡态交通流,相对于流通量间断LWR(Lighthill-Whitham-Richards)模型,其能更好地刻画实际交通现象.Under inhomogeneous road conditions, a conserved high-order (CHO) anisotropic traffic flow model was extended to obtain a CHO model with discontinuous fluxes. Based on the property of the Riemann invariant for the CHO model with discontinuous fluxes, the first-order Godunov, EO (Engquist-Osher) and LF (Lax-Friedrichs) numerical schemes for this model were designed with the local simplification method and the δ mapping algorithm. The numerical simulations show that, the CHO model with discontinuous fluxes is reasonable and effective. It can describe equilibrium and non-equilibrium traffic flows, and can better describe the actual traffic phenomena compared with the LWR (Lighthill-Whitham-Richards) model with a discontinuous flux.

关 键 词：流通量间断CHO模型 Riemann不变量 局部简化 δ映射 

分 类 号：O29[理学—应用数学]