项目名称: 燃烧流和交通流的初边值问题
项目编号: No.11301264
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 潘丽君
作者单位: 南京航空航天大学
项目金额: 22万元
中文摘要: 燃烧流和交通流,其基本方程均是非线性双曲守恒律方程。研究该类方程的初边值问题,对于揭示燃烧和交通现象中的规律和性质,在理论及应用方面都具有重要的意义。 本课题研究气体动力学ZND燃烧模型的Riemann问题,该问题是燃烧问题的重点和难点。通过对反应区内特征线的研究,构造出上述问题的解析解。研究ZND模型的广义Riemann问题、波的相互作用问题及初边值问题,揭示爆燃向爆轰转化、点火、熄火现象。利用特征分析法和熵流对理论,研究压力函数为Chaplygin方程的AR交通模型的初边值问题。分别研究凸和非凸、不带相变和带有相变的AR模型的Riemann问题、广义Riemann问题、波的相互作用问题及初边值问题。交通流模型的非凸性和耦合性,将会给理论分析和数值模拟带来极大的困难。我们将得到上述问题解的存在性、稳定性等,进而利用该结果刻画交通信号灯、交通瓶颈堵塞和交通相变特性的改变等各种交通现象。
中文关键词: ZND燃烧模型;AR交通流模型;Riemann 问题;特征线;熵流对
英文摘要: The models of combustion flow and traffic flow are nonlinear conservation laws. In order to reveal the traffic phenomena and combustion phenomena, etc., we will study the initial boundary value problem for the nonlinear hyperbolic conservation laws. It is meaningful to do this work in both theory and applications. The Riemann problem for the gas dynamics Zeldovich-von Neumann-Doring(ZND) combustion model is the key and difficult point of the combustion problems. The analytical solutions of the problem will be constructed by analyzing characteristics in the reaction zone. We will study the generalized Riemann problem,the wave interaction problem and the initial boundary value problem for the ZND model to reveal the following combustion phenomena: the transition from deflagration to detonation, ignition phenomena and flameout phenomena. With the method of characteristic analysis and the theory of entropy-flux pair, we will consider the initial boundary value problem for the Aw-Rascle(AR) traffic model with Chaplygin pressure. Furthermore, we will study the Riemann problem, the generalized Riemann problem, the wave interaction problem and the initial boundary value problem for the convex and non-convex AR traffic model, and the AR model with phase transitions. Due to the non-convexity and the coupling of the traf
英文关键词: ZND combustion model;AR traffic model;Riemann problem;characteristics;entropy-flux pair