摘要：行人系统是一个具有较强非线性相互作用的多粒子复杂系统,行人交通受自我意志的支配，但行人流的研究不能只分析单独行人的行走特点，需要对多个具有复杂行走特性的行人所组成的行人流，通过个体之间非线性相互作用演变成的宏观集群运动进行分析，所以想要对行人流进行研究需要涉及到动力学、心理学、社会学等等，需要多种学科，不同领域的结合。对行人流问题的研究，国内外许多学者通常使用建模的方法。早期的研究中，由于当时的技术限制，学者只能采用宏观模型模拟行人流。通常使用流体力学的方法来模拟行人流，行人流的流力力学模型是典型的宏观模型，宏观模型通常适用于较大人群，把人群看作一个整体，行人流的宏观特性就是行人流量、行人密度和人流平均速度之间的关系，模拟行人状态变化，通常使用微分方程来描述三者之间的关系。近几年，微观模型方法受到更多学者的重视，微观模型将行人视为一种特殊的颗粒流动，注重对个体行为与群体行为之间关系，研究人与人之间的相互作用。

本文主要研究宏观模型下行人流的整体行为。利用数值模拟的手段，研究瓶颈问题中行人流动力学的流场变化规律。数值方法上采用了计算流体力学方程组的高精度松弛数值格式，该方法在瓶颈问题中的应用尚属首次。

关键词： 行人流宏观模型，微分方程，数值格式

Numerical Simulation of Macroscopic Control Equation for Pedestrian Flow

Abstract: Pedestrian system is a strong nonlinear complex interaction of many particle system, pedestrian traffic at the mercy of the self will, but the line flow analysis, the research of characteristics of pedestrian walking alone, need for multiple with complex characteristics of pedestrians do stream of people, walking through the nonlinear interaction between the inpidual into macroscopic cluster movement is analyzed, so want to study of line of stream of people need to involve dynamics, psychology, sociology and so on, need a variety of subjects, the combination of different fields. The research on pedestrian flow problem is usually used by many scholars at home and abroad. In the early studies, due to the limitations of the technology at that time, scholars could only use the macro model to simulate the flow of people. Usually fluid mechanics method is used to simulate the flow, flow force mechanics model of line flow is a typical macro models, macroscopic model usually apply to the larger population, the population as a whole, macro characteristic of line flow is the pedestrian traffic, pedestrian density and flow, the relationship between the average speed of simulation of pedestrian state changes, usually USES differential equation to describe the relationship between the three. Thought highly of by more and more scholars in recent years, the microscopic model method, the microscopic model pedestrians is regarded as a special kind of particle flow, pay attention to the relationship between inpidual behavior and group behavior, study the interaction between people, simulate macroscopic with microscopic model.

This paper mainly studies the overall behavior of pedestrian flow under macroscopic model. Use the method of numerical simulation, study the different boundary conditions downward flow dynamic change law of flow field and discuss the effects of the numerical format of the final numerical results, analysis facility structure on the influence of the line of people to evacuate.

Key words: pedestrian flow macroscopic model, differential equation, numerical format

目录

1 绪论 4

1.1 研究背景及意义 4

1.2 宏观行人流模型国内外相关文献综述 5

1.3 研究对象及主要内容 5

1.4 研究方法 7

2 模型 7

3 算法 9

3.1 快速扫描方法 9

3.2 松弛格式和WENO格式 9