交通流宏观模型的非线性密度波研究

发布时间：2018-01-24 21:15

本文关键词： 交通流流体力学模型格子流体力学模型 KdV方程 KdV-Burgers方程　出处：《宁波大学》2014年硕士论文　论文类型：学位论文

【摘要】：本文旨在研究交通流宏观模型的非线性密度波，基于现有的微观跟驰模型，根据宏观与微观变量之间的关系，提出修正的宏观模型，并进行合理分析和计算机模拟。主要研究内容如下：一、改进的速度梯度模型中的KdV-Burgers方程。基于全速度模型，通过宏、微观变量的转换关系并采用Taylor展开至二阶得到新的速度梯度模型，并保持了各向异性特性。经过线性分析获得了中性稳定曲线，并在其附近得到了KdV-Burgers方程来描述交通流非线性密度波，而在以前的模型中很难得到该方程。我们对模型进行数值模拟，给出了不同初始密度条件下密度波的时间演化图，其与理论结果相一致。二、考虑司机预测效应的流体力学模型。在实际交通生活中，，司机的开车行为会对交通流带来很大的影响，郑等人考虑司机预测效应，提出了新的有效模型，我们采用更加精确的车头间距与密度关系得到了相应的宏观模型。我们对新模型进行理论分析得到了KdV方程，并作了相应的数值模拟；接着，我们提出了带有考虑司机预测效应的双速度差模型，并推导出宏观模型。我们也对新模型做了相关分析，具体得到KdV-Burgers方程，以及适当的预测时间能提高交通流稳定性的结论。三、考虑预测效应的双车道流体力学模型。本章借鉴Nagatani的思想，考虑司机预测效应，并建立差分与微分方程的联系得到了相应的双车道流体力学模型。现如今，人们对单车道连续性模型作非线性分析的较多，而对双车道连续模型的很少，大多数重点对模型作数值模拟。我们不仅对新模型进行了线性分析，而且还通过非线性分析得到了描述双车道连续性模型非线性密度波的KdV-Burgers方程。
[Abstract]:The purpose of this paper is to study the nonlinear density wave of traffic flow macroscopic model. Based on the existing microscopic car-following model and the relationship between macro and micro variables, a modified macroscopic model is proposed. Reasonable analysis and computer simulation are carried out. The main research contents are as follows: The first is the KdV-Burgers equation in the improved velocity gradient model. Based on the full speed model, a new velocity gradient model is obtained by the transformation of macro and micro variables and the Taylor expansion to the second order. The neutral stability curve is obtained by linear analysis and the KdV-Burgers equation is obtained near it to describe the nonlinear density wave of traffic flow. But it is difficult to obtain the equation in the previous model. The numerical simulation of the model is carried out, and the time evolution diagram of the density wave under different initial densities is given, which is in agreement with the theoretical results. Second, a hydrodynamic model considering driver prediction effect. In the actual traffic life, driver's driving behavior will have a great impact on the traffic flow. Zheng et al. considered the driver prediction effect, and put forward a new effective model. We get the corresponding macroscopic model by using the more accurate relation between the headspace and the density. We get the KdV equation by theoretical analysis of the new model and make the corresponding numerical simulation. Then, we put forward a two-speed difference model with driver prediction effect, and derived a macro model. We also made a correlation analysis of the new model, and got the KdV-Burgers equation. And the conclusion that the traffic flow stability can be improved by proper prediction time. Third, a two-lane hydrodynamic model considering predictive effects. This chapter draws lessons from Nagatani's thought, considers the driver forecast effect, and establishes the difference and the differential equation connection to obtain the corresponding two-lane fluid dynamics model. People do more nonlinear analysis of single-lane continuity model, but few of two-lane continuous model, most of them focus on numerical simulation. We not only do linear analysis on the new model. Furthermore, the KdV-Burgers equation describing the nonlinear density waves of the two-lane continuity model is obtained by nonlinear analysis.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U491.112

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