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.

中文翻译：

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宏观自动驾驶车辆交通流模型解近似数值方法的比较研究


在本文中，使用粒子方法对自动驾驶汽车的“流体状”宏观交通流模型进行近似解。结果表明，这种方法保留了适用于宏观交通模型的某些微分不等式：质量保持不变，机械能衰减，能量泛函也在衰减。为了证明所考虑的粒子方法的优势，本文提供了与粘性可压缩流体模型的其他数值方法的比较。由于宏观交通模型的解可以用由单个非线性热型偏微分方程组成的简化模型的解来近似，因此还将粒子法生成的数值解与简化模型的数值解进行比较。最后，给出了交通仿真场景并与 Aw-Rascle-Zhang （ARZ） 模型进行了比较，说明了使用自动驾驶汽车的优势。