In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a nonlocal constraint on the flux. The constraint level depends on the trajectory of the slower vehicle which is given by an ODE depending on the downstream traffic density. After proving well-posedness, we first build a finite volume scheme and prove its convergence, and then investigate numerically this model by performing a series of tests. In particular, the link with the limit local problem of [M. L. Delle Monache and P. Goatin, J. Differ. Equ. 257 (2014), 4015–4029] is explored numerically.

中文翻译：

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慢速行驶的车辆对交通的影响：轻度非局部模型的适定性和近似

在本文中，我们提出了一个宏观模型，该模型描述了慢速行驶的大型车辆对道路交通的影响。该模型由对通量具有非局部约束的标量守恒定律组成。约束水平取决于较慢的车辆的轨迹，该轨迹由ODE给出，取决于下游交通密度。在证明了适当的姿势之后，我们首先建立一个有限体积的方案并证明其收敛性，然后通过执行一系列测试对这个模型进行数值研究。特别是，与[ML Delle Monache和P. Goatin，J. Differ。等式 257（2014），4015–4029]进行了数值研究。