基于Riemann问题的交通网络流体力学建模与数值求解

项目名称： 基于Riemann问题的交通网络流体力学建模与数值求解

项目编号： No.11272199

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 张鹏

作者单位： 上海大学

项目金额： 82万元

中文摘要： 通过研究守恒高阶(CHO)模型和多车种LWR模型的交叉口Riemann问题，得到在交叉口处CHO模型齐次方程的准确Riemann解或Godunov型数值流通量，以及多车种LWR模型的Riemann近似解或近似数值流通量，从而可以构造这两类模型求解网络交通流的一阶和高阶数值格式。将上述两类模型由目前只能求解路段推广到能求解网络，其主要意义是使它们能够应用于求解动态交通分配问题。由于CHO模型能够合理描述交通流不稳定现象，如时停时走波；多车种LWR模型可描述不同车型混流和超车，上述推广应用将改进现有动态交通分配模型的合理性和适用性，有力推动涵盖极广的相关问题，如信号灯控制、交通系统可靠性分析和敏感性分析等方面的研究进展，并为智能交通系统的建设和管理提供理论依据。由于交叉口Riemann问题是经典Riemann问题的推广，课题的开展还将丰富计算流体力学和守恒律方程理论的研究内容。

中文关键词： 城市路网；交通流高阶模型；交叉口Riemann问题；均衡原理；行人流

英文摘要： Dynamic traffic assignment (DTA) problems serve as a theoretical fundamental for the establishment of the intelligent transportation system (ITS). For the passing decade, the cell-transmission (CT) model has gradually replaced the TRANSYT model for the simulation of traffic flow in DTA problems, because of its ability to describe the propagation of queue within a road section or across a junction. However, as a discrete version of the LWR model, the CT model is only able to describe the equilibrium traffic phase. That is, it simply assumes a fixed velocity-density curve in the phase plane, which does not well agree with the observation. Actually, there have been more advanced models proposed, such as the higher-order model and the multi-class model, which better depict traffic flow phenomena. Nevertheless, currently these models are only able to simulate traffic flow on a single road and therefore cannot be directly used to solve DTA problems which involve a traffic network, unless the boundary conditions at a node or junction for the homogeneous equations of these models are appropriately derived. Here, the boundary conditions refer to the numerical fluxes, which are essential to the design of a numercal scheme for soving the network. Solution for such boundary conditions gives rise to a Junction Riemann (JR)

英文关键词： urban road networks；higher-order traffic flow model；Riemann problem at a junction；equilibrium principle；pedestrian flow