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A Macroscopic Traffic Flow Model Accounting for Bounded Acceleration
SIAM Journal on Applied Mathematics ( IF 1.9 ) Pub Date : 2021-02-02 , DOI: 10.1137/19m1268173
Nicolas Laurent-Brouty , Guillaume Costeseque , Paola Goatin

SIAM Journal on Applied Mathematics, Volume 81, Issue 1, Page 173-189, January 2021.
This paper details a new macroscopic traffic flow model accounting for the boundedness of traffic acceleration, which is required for physical realism. Our approach relies on the coupling between a scalar conservation law, which refers to the seminal Lighthill--Whitham--Richards model, and a system of ordinary differential equations describing the trajectories of accelerating vehicles, which we treat as moving constraints. We propose a wave-front tracking algorithm to construct approximate solutions. We use this algorithm to prove the existence of entropy weak solutions to the associated Cauchy problem and provide some numerical simulations illustrating the solution behaviour.


中文翻译:

有限加速的宏观交通流模型

SIAM应用数学杂志,第81卷,第1期,第173-189页,2021年1月。
本文详细介绍了一种新的宏观交通流模型,该模型考虑了交通加速的局限性,这是物理现实性所必需的。我们的方法依赖于标量守恒定律之间的耦合,标量守恒定律是指开创性的Lighthill-Whitham-Richards模型与描述加速车辆轨迹的常微分方程组,我们将其视为运动约束。我们提出了一种波前跟踪算法来构造近似解。我们使用该算法证明了相关柯西问题的熵弱解的存在,并提供了一些数值模拟来说明解的行为。
更新日期:2021-02-17
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