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多等级交通流LWR模型的双曲性和Riemann不变量
发表时间：2009-01-15 浏览量：2649 下载量：908
| 全部作者： | 杨建伟，王可，王红利 |
| 作者单位： | 北京工业大学应用数理学院；包头师范学院数学科学学院 |
| 摘 要： | 随着社会的发展，对交通流的研究变得越来越重要。本文基于一阶双曲守恒律的相关理论，对多等级交通流LWR模型，即multi-class Lighthill-Whitham-Richards（简记为MCLWR）模型进行了研究。用两种方法给出了该模型在不同情形下双曲性的数学证明，运用特征线方法研究并计算了任意等级MCLWR交通流模型的Riemann不变量，得到了其传递的交通信息，给出了Riemann不变量物理意义的解释，即总密度保持不变和相对密度保持不变，最后又从形式上指出了在多等级车流并行时，MCLWR与LWR两种交通流模型实际上是等价的。 |
| 关 键 词： | 应用数学；双曲性；双曲守恒律；多等级交通流LWR模型；Riemann不变量 |
| Title： | Hyperbolicity and Riemann invariants of a multi-class traffic flow Lighthill-Whitham-Richards model |
| Author： | YANG Jianwei, WANG Ke, WANG Hongli |
| Organization： | College of Mathematical and Physical Sciences, Beijing University of Technology; School of Mathematic Science, Baotou Teacher’s Couege |
| Abstract： | With the further development of society, the study on traffic flow becomes more and more important. This paper studies a traffic flow multi-class Lighthill-Whitham-Richards model (MCLWR) based on the theory of one-order hyperbolic conservation laws. Mathematic proof of the hypertonicity for this model is given using two different cases. Furthermore, the Riemann invariants for the multi-class traffic flow LWR model are studied by using characteristic line method, and the physical interpret of the Riemann invariants are also pointed out. The information in transfer is obtained, that is, the total density and the relative density hold the same. Finally, the coherence between MCLWR model and LWR model is shown when the multi-class vehicle flow almost run at the same velocity. |
| Key words： | applied mathematics; hyperbolicity; hyperbolic conservation laws; multi-class traffic flow Lighthill-Whitham-Richards model; Riemann invariants |
| 发表期数： | 2009年1月第1期 |
| 引用格式： | 杨建伟，王可，王红利. 多等级交通流LWR模型的双曲性和Riemann不变量[J]. 中国科技论文在线精品论文，2009，2（1）：25-32. |
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