一种用于微观和宏观交通流模型的混合数值方法
A hybrid numerical method for a microscopic and macroscopic traffic flow model
AI总结：
本文提出了一种混合数值方法，用于改进微观和宏观交通流模型，通过引入新的变量重新表述经典模型并验证其理论一致性。
摘要：
本文介绍了一种基于微观跟随者模型的交通流模型，同时对流的密度和速度施加最大约束。相关的宏观模型可以表示为守恒形式。通过引入一个随流传播的变量up，其中p是速度偏移，u是相对速度，我们将经典的Aw-Rascle-Zhang（ARZ）模型和改进的Aw-Rascle模型重新表述，以描述真实的基本图。导出了基本波，并通过求解黎曼问题来验证模型的理论一致性。我们进一步扩展到二维模型。通过使用混合的Godunov-Glimm方案对一维和二维情况进行了数值模拟，以验证模型的性能。
英文摘要：
In this paper, we introduce a traffic flow model based on a microscopic follow-the-leader model, while enforcing maximal constraints on the density and velocity of the flow. The related macroscopic model can be represented in conservative formulation. By introducing an advected variable up with the flow, where p is the velocity offset, and u is the relative velocity, we reformulate the classical Aw-Rascle-Zhang (ARZ) model and the modified Aw-Rascle model to describe a realistic fundamental diagrams. The elementary waves are derived, and the Riemann problem is solved to validate the model's theoretical consistency. We further extend to a two-dimensional model. Numerical simulations are given for both one-and two-dimensional case by using the hybrid Godunov-Glimm scheme to verify the model's performance.
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