Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models.
Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models.
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DOI：
10.1103/physreve.74.026109
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发表时间：
2006-08
期刊：
影响因子：
--
通讯作者：
Peng Zhang;Sze Chun Wong
中科院分区：
文献类型：
--
作者：
Peng Zhang;Sze Chun Wong
本文揭示了应用弱解理论求解Payne-Whitham（PW）模型中宽团簇行波解时守恒形式的本质。考虑加速度方程的守恒形式是高阶交通流模型发展中的一个重要组成部分，但在研究界却很大程度上被忽视。为了解决这个问题，我们对同一个PW模型定义了两种守恒形式，从而得到了两种具有不同宽团簇特征参数的解。分析结果与数值模拟结果吻合较好。此外，这两个解决方案也被证明是渐近的著名的Kühne和Kerner-Konhaüser模型与粘度项。更重要的是，对加速度方程守恒形式的仔细处理填补了文献中的重要空白。如果没有守恒形式，所得到的解在很大程度上取决于数值格式的设计，并且可能是相当任意的，并且可能不充分符合物理相关性质。
This paper shows the essence of conservation forms when applying the weak solution theory to solve the traveling wave solution of a wide cluster in the Payne-Whitham (PW) model. The consideration of the conservation form for the acceleration equation is an important ingredient in the development of higher-order traffic flow models, but it is largely ignored in the research community. To fix the idea, we define two conservation forms for the same PW model, and consequently derive two solutions with different sets of characteristic parameters of the wide cluster. The analytical results are in good agreement with those that are obtained from numerical simulations. Moreover, these two solutions are also shown to be asymptotic to those of the well-known Kühne and Kerner-Konhaüser models with a viscosity term. More importantly, the careful treatment of the conservation form for the acceleration equation closes the important gap in the literature. Without the conservation form, the solution obtained depends very much on the design of numerical schemes, and can be quite arbitrary and may not adequately conform to the physically relevant properties.