标题： 中心迎风格式用于相变交通流模型 显示英文标题

标题： Central-Upwind Scheme for the Phase-Transition Traffic Flow Model

摘要： 相变模型是一类重要的非平衡连续交通流模型，具有复制复杂交通现象、保持各向异性以及容纳自动驾驶车辆的潜力等特性。 然而，它们的复杂数学特性，如不连续解域，带来了数值挑战，并限制了它们在交通流理论中的探索。 本文专注于开发一种针对相变交通流模型的稳健且精确的数值方法：我们提出了一种专为不连续相变模型设计的二阶半离散中心迎风格式。 该新方案结合了对适当流域的投影，确保了对不连续性的增强处理，并保持了物理一致性和准确性。 我们通过大量且具有挑战性的数值测试展示了所提出方案的有效性，展示了其在相变交通流建模中进一步研究和应用的潜力。 相变模型能够将“时间间隔”——自动驾驶交通控制中的关键要素——作为守恒变量嵌入其中，这与自动驾驶车辆的控制逻辑无缝对接，显示出未来应用的重大潜力，而所提出的数值方案现在大大促进了对这些潜力的探索。 显示英文摘要

摘要： Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated vehicles. However, their complex mathematical characteristics such as discontinuous solution domains, pose numerical challenges and limit their exploration in traffic flow theory. This paper focuses on developing a robust and accurate numerical method for phase-transition traffic flow models: We propose a second-order semi-discrete central-upwind scheme specifically designed for discontinuous phase-transition models. This novel scheme incorporates the projection onto appropriate flow domains, ensuring enhanced handling of discontinuities and maintaining physical consistency and accuracy. We demonstrate the efficacy of the proposed scheme through extensive and challenging numerical tests, showcasing their potential to facilitate further research and application in phase-transition traffic flow modeling. The ability of phase-transition models to embed the ``time-gap'' -- a crucial element in automated traffic control -- as a conserved variable aligns seamlessly with the control logic of automated vehicles, presenting significant potential for future applications, and the proposed numerical scheme now substantially facilitates exploring such potentials.