In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the macroscopic traffic model: mass is preserved, the mechanical energy is decaying and an energy functional is also decaying. To demonstrate the advantages of the particle method under consideration, a comparison with other numerical methods for viscous compressible fluid models is provided. Since the solutions of the macroscopic traffic model can be approximated by the solutions of a reduced model consisting of a single nonlinear heat-type partial differential equation, the numerical solutions produced by the particle method are also compared with the numerical solutions of the reduced model. Finally, a traffic simulation scenario and a comparison with the Aw-Rascle-Zhang (ARZ) model are provided, illustrating the advantages of the use of automated vehicles.

翻译：本文采用粒子方法逼近自动车辆"类流体"宏观交通流模型的解。研究表明，该方法能保持宏观交通模型成立的若干微分不等式：质量守恒、机械能衰减以及能量泛函衰减。为论证该粒子方法的优势，本文将其与粘性可压缩流体模型的其他数值方法进行了比较。由于宏观交通模型的解可通过由单个非线性热型偏微分方程构成的简化模型解进行逼近，因此本文还将粒子方法生成的数值解与该简化模型的数值解进行了对比。最后，通过交通仿真场景并与Aw-Rascle-Zhang(ARZ)模型进行对比，展示了自动车辆应用的优越性。