SIAM Journal on Applied Mathematics, Volume 80, Issue 1, Page 639-656, January 2020.
We consider a model describing the presence of a platoon of vehicles moving in the traffic flow. The model consists of a coupled PDE-ODE system describing the interaction between the platoon and the surrounding traffic flow. The scalar conservation law takes into account the main traffic evolution, while the ODEs describe the trajectories of the initial and final points of the platoon, whose length can vary in time. The presence of the platoon acts as a road capacity reduction, resulting in a space-time discontinuous flux function. We describe the solutions of Riemann problems and design a finite volume numerical scheme sharply capturing nonclassical discontinuities. Some numerical tests are presented to show the effectiveness of the method.

中文翻译：

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公路交通编排的宏观模型

SIAM应用数学杂志，第80卷，第1期，第639-656页，2020年1月。
我们考虑一个模型，该模型描述了在交通流中行驶的车辆排的存在。该模型由一个耦合的PDE-ODE系统组成，该系统描述了排与周围交通流之间的相互作用。标量守恒定律考虑了主要交通量的演变，而ODE则描述了排的起点和终点的轨迹，其长度会随时间变化。排的存在会降低道路通行能力，从而导致时空不连续通量函数。我们描述了黎曼问题的解决方案，并设计了一个有限体积的数值方案，可以清晰地捕获非经典的不连续性。进行了一些数值测试，证明了该方法的有效性。