交通流Aw-Rascle模型相关问题的研究

发布时间：2018-05-22 19:57

本文选题：Aw-Rascle模型 + Riemann问题　；参考：《上海大学》2014年博士论文

【摘要】：本文主要研究一维交通流Aw-Rascle模型在信号灯处的流动问题以及在Chaplygin气体压力下具有广义熵条件Aw-Rascle模型的Riemann问题和输运方程带有delta函数初值的Riemann问题.第二章首先介绍了关于双曲型守恒律方程组的一些基本概念,继而对一维双曲守恒律方程组的一般理论做了简要的介绍,为后面章节的讨论作准备.第三章研究了对于单一通道上信号灯处的流动问题.我们利用Aw-Rascle模型和一些交通规则(在红灯时间下汽车必须停下来不动以及汽车之间有安全间隙不发生碰撞)来分析和演化信号灯不断变化时汽车穿过信号灯时的流动问题.我们建立了激波能否穿过信号灯处交界线的准则并给出了临界值tc的表达式.为了使激波能穿过交界线,并且使信号灯能自由地操控,绿灯时间必须超过这个临界值.更进一步,我们证明了交通流量在信号灯处达到最大值.最后,我们给出了与理论结果和实际交通情况相符的数值例子.第四章研究了在Chaplygin气体压力下具有广义熵条件的Aw-Rascle模型的Riemann问题.在广义Rankine-Hugoniot关系和δ-熵条件以及广义δ-熵条件下构造了模型的整体解.在一些解中我们定义了一种新的由初始delta函数产生的delta波-原发型delta波,它满足广义Rankine-Hugoniot关系和广义δ-熵条件.这种原发型的delta的强度可能随着时间的增大变得越来越大也可能在有限的时间里消失.第五章研究了带有delta初值的输运方程的Riemann问题.我们构造了在广义Rankine-Hugoniot关系和δ-熵条件下的全局整体解.更进一步,通过对初值的扰动我们得到了广义解的稳定性.
[Abstract]:In this paper, the flow problem of one-dimensional traffic flow Aw-Rascle model at the signal light, the Riemann problem of the Aw-Rascle model with generalized entropy condition and the Riemann problem of the transport equation with the initial value of delta function under the pressure of Chaplygin gas are studied. In the second chapter, some basic concepts of hyperbolic conservation law equations are introduced, and then the general theory of one-dimensional hyperbolic conservation law equations is briefly introduced. In the third chapter, the flow problem of the signal lights on a single channel is studied. We use the Aw-Rascle model and some traffic rules (the car must stop at red light and there is a safety gap between cars to not collide) to analyze and evolve the flow problem of the vehicle passing through the signal light when the signal light is constantly changing. We establish the criterion of whether the shock wave can cross the junction of the signal lamp and give the expression of the critical value TC. In order for the shock to cross the junction and to allow the signal to operate freely, the green time must exceed this threshold. Furthermore, we have proved that the traffic flow reaches the maximum at the signal light. Finally, we give a numerical example which is consistent with the theoretical results and the actual traffic conditions. In chapter 4, the Riemann problem of Aw-Rascle model with generalized entropy condition under Chaplygin gas pressure is studied. The global solution of the model is constructed under the generalized Rankine-Hugoniot relation, 未 -entropy condition and the generalized 未 -entropy condition. In some solutions, we define a new delta wave-primitive delta wave generated by the initial delta function, which satisfies the generalized Rankine-Hugoniot relation and the generalized 未 -entropy condition. The strength of the original delta may grow larger over time or disappear in a limited amount of time. In chapter 5, we study the Riemann problem of transport equation with delta initial value. We construct the global solution under the generalized Rankine-Hugoniot relation and 未-entropy condition. Furthermore, we obtain the stability of the generalized solution by perturbation of the initial value.
【学位授予单位】：上海大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：U491.112

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