AI 中文总结
该研究提出二维二阶宏观交通流模型，耦合纵向与横向相互作用，基于FVDM和OVM构建，纳入道路边界效应，经数值实验可再现无序交通关键特征，为分析二维车辆流提供基础。
AI 中文摘要
本研究提出了一种二维二阶宏观交通流模型，通过明确纳入纵向与横向耦合相互作用来捕捉无序交通的复杂动力学。该框架将经典连续性方程扩展至二维空间，并引入由自驱动、相互作用诱导及道路边界相关分量组成的加速度方程。宏观纵向加速度基于全速度差模型（Full Velocity Difference Model, FVDM）构建，而横向动力学则由与最优速度模型（Optimal Velocity Model, OVM）一致的相互作用原理支配。道路边界效应的明确纳入，使其能够表征无车道及弱车道规则交通系统中至关重要的车辆约束与空间共享行为。通过一系列数值实验对该模型进行检验，实验中在一系列初始条件下，分别分析纵向与横向动力学，并在耦合二维场景中同时分析二者，初始条件包括自由流、中等拥堵与严重拥堵之间的转变，以及不同的横向密度配置。模拟结果表明，该模型能够再现关键交通特征，如激波传播、横向分散、车辆重排及沿道路宽度的稳定密度演化。基于迎风与Lax-Friedrichs离散化的数值格式，确保耦合偏微分方程的稳定解。总体而言，所提出的框架为无序交通提供了稳健的宏观描述，并为分析二维车辆流动力学提供了一致基础。
英文摘要
In this study, a two-dimensional second-order macroscopic traffic flow model is proposed to capture the complex dynamics of disordered traffic by explicitly incorporating coupled longitudinal and lateral interactions. The framework extends the classical continuity equation to two spatial dimensions and introduces acceleration equations consisting of self-driven, interaction-induced, and road-boundary-related components. The macroscopic longitudinal acceleration is formulated based on the Full Velocity Difference Model (FVDM), while lateral dynamics are governed by interaction principles consistent with the Optimal Velocity Model (OVM). The explicit inclusion of road-boundary effects enables the representation of vehicle confinement and space-sharing behavior that are essential in lane-free and weakly lane-disciplined traffic systems. The model is examined through a series of numerical experiments in which longitudinal and lateral dynamics are analysed individually as well as simultaneously within a coupled two-dimensional setting under a range of initial conditions, including transitions between free-flow, medium congestion, and heavy congestion, and different lateral density configurations. The simulations demonstrate the model's ability to reproduce key traffic features such as shockwave propagation, lateral dispersion, vehicle rearrangement, and stable density evolution across the road width. The numerical scheme, based on upwind and Lax-Friedrichs discretisations, ensures stable solutions of the coupled partial differential equations. Overall, the proposed framework provides a robust macroscopic description of disordered traffic and offers a consistent basis for analysing two-dimensional vehicular flow dynamics.
Comments44 pages, submitted to Transp. Res. Part B
