宏观预测型动态网络交通流分配模型及其算法的研究

This research project aims at the modeling and numerical simulation of the macroscopic predictive dynamic traffic assignment (DTA) problem with two major objectives. First, it proposes two-dimensional hydrodynamic models (the mass conservation for traffic flow on networks, or together with a "momentum" conservation) under the continuum hypothesis, which are coupled with a path-choice strategy based on the predictive dynamic user optimization (PDUO); the mathematical properties of the models, such as the stability and the existence of the viscous solutions, are investigated. Second, the high resolution numerical schemes, including the finite difference scheme on structured grids and the finite volume scheme coupled with a finite element scheme on unstructured grids, are developed for solving the proposed models. These proposed models and numerical schemes are adopted to simulate typical DTA problems, e.g.,the flow assignment problem in a polycentric urban traffic network with multiple central business districts (CBDs), in an attempt to capture the dynamic and macroscopic features of traffic networks, the collective behavior or overall characteristic of traffic users, and the mechanism of the jamming and dissipation. Since the proposed models possess strong nonlinearity and complex physical effects with several coupled equations, the developed analytical tools and numerical schemes together with the achieved friuts under this project will promote the development in such disciplines as the traffic science, computational mathematics and fluid mechanics.

本项目从以下两个方面研究宏观预测型动态网络交通流分配模型及其数值方法。一、基于连续介质理论建立平面区域内预测型动态网络交通流均衡与非均衡分配问题的流体力学模型（网络交通流的质量守恒方程、预测型动态用户最优路径选择条件等耦合而成的复杂非线性双曲型偏微分方程组），并讨论模型的数学性质，如模型稳定性、粘性解存在性等。二、针对构建的流体力学模型，设计高分辨率数值求解方法，如结构网格上有限差分方法与非结构网格上有限体积/有限元耦合方法，并将模型及其数值方法用于求解典型的城市交通分配问题，如多中心城市交通网络的流量分配问题，以研究网络交通流的动态、宏观特性，用户整体平均交通行为，以及交通拥挤形成与消失机理等。由于所提出的模型具有强非线性、复杂物理效应以及多方程耦合等特征，需要发展新的解析工具和数值计算方法，本项目的研究内容和所取得的研究成果将促进交通科学、计算数学和流体力学等学科的发展。

随着城市交通系统日趋动态化、密度化、网络化，交通科学对宏观交通流理论的需求日益迫切。对于交通拥堵、路段密集和规模庞大的单（多）用户等级城市交通系统，动态网络交通流的宏观研究方法具有重要的理论价值和现实意义。本项目开展了大规模复杂城市交通系统中预测型动态网络交通流均衡与非均衡分配问题的流体力学建模及其数值方法的研究。研究了单（多）用户等级网络交通流的宏观特性，如网络交通流密度、平均速度和流量等，交通用户整体平均路径选择行为特点，交通拥挤形成与消失机理，以及走走停停波等各种非线性动力学现象等。所得结果为城市交通系统的合理规划与设计，网络交通流的有效管理与控等提供了科学依据，同时促进了交通科学，计算数学和流体力学多个学科的发展。在项目实施过程中，发表SCI检索论文5篇，其中1篇发表在交通类顶级期刊《Transportation science》上，另4篇发表在计算机类、物理类、交通类国际SCI期刊上，发表EI检索论文4篇；参加3次国内国际学术会议，并在2次会议上做分组报告。