多类动力学交通流模型：离散速度公式与扩散修正的宏观极限
A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits
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中文总结 AI 辅助
本文提出基于Prigogine-Herman框架的多类离散速度动力学交通流模型，推导相关双曲标度方程组，采用路径守恒有限体积格式数值近似，得到扩散修正多类宏观模型并通过单车道模拟验证理论结果。
中文摘要 AI 辅助
本文基于非局部Prigogine-Herman框架，提出了离散速度动力学交通流模型的多类扩展。我们从连续动力学公式推导了双曲标度方程组，该方程组通过制动和松弛项描述不同车辆类别的交互作用。随后对速度变量进行离散化以处理任意数量的车辆类别，并分析所得公式的结构特性，尤其证明了双曲性和总线性退化性。由于模型具有非保守结构，我们采用路径守恒有限体积格式对该系统进行数值近似。最后，推导了对应的扩散修正多类宏观模型，研究其稳定性并在单车道道路上开展数值模拟，以阐释理论结果。
英文摘要
This paper introduces a multi-class extension of a discrete-velocity kinetic traffic flow model based on a non-local Prigogine-Herman framework. We derive a hyperbolically scaled system of equations from a continuous kinetic formulation describing interactions between different vehicle classes through braking and relaxation terms. The model is then discretized with respect to the velocity variable for an arbitrary number of vehicle classes, and the structural properties of the resulting formulation are analyzed. In particular, we prove hyperbolicity and total linear degeneracy. Due to the non-conservative structure of the model, we employ a path-conservative finite volume scheme for the numerical approximation of the system. Finally, we derive the corresponding diffusively-corrected macroscopic multi-class model, investigate its stability and present numerical simulations on a single-lane road to illustrate the theoretical findings.
