| 流通量间断守恒高阶交通流模型及其数值模拟 |
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| 引用本文： | 乔殿梁,李晓洋,郭明旻,张鹏.流通量间断守恒高阶交通流模型及其数值模拟[J].应用数学和力学,2019,40(5):546-561. |
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| 作者姓名： | 乔殿梁 李晓洋 郭明旻 张鹏 |
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| 作者单位： | 1上海大学 上海市应用数学和力学研究所, 上海 200072;2复旦大学 航空航天系, 上海 200433;3上海市力学在能源工程中的应用重点实验室, 上海 200072 |
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| 基金项目： | 国家自然科学基金（面上项目)(11672348;11272199)；国家重点研发计划(2018YFB1600900);国家重点基础研究发展计划(973计划)(2012CB725404) |
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| 摘 要： | 在非均匀道路条件下，推广了各向异性守恒高阶交通流模型(CHO模型)，获得流通量间断CHO模型，并基于其Riemann不变量性质，运用局部简化方法及δ映射算法，设计了求解流通量间断CHO模型的一阶Godunov、EO(Engquist-Osher)和LF(Lax-Friedrichs)等数值格式.通过数值模拟表明流通量间断CHO模型是合理有效的，它可以描述平衡态和非平衡态交通流，相对于流通量间断LWR(Lighthill-Whitham-Richards)模型，其能更好地刻画实际交通现象.
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| 关 键 词： | 流通量间断CHO模型 Riemann不变量 局部简化 δ映射 |
| 收稿时间： | 2018-11-01 |
A Conserved High Order Traffic Flow Model With Discontinuous Flux and Its Numerical Simulation |
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| Affiliation: | 1Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China;2Department of Aeronautics and Astronautics,Fudan University, Shanghai 200433, P.R.China;3Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, P.R.China |
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| Abstract: | Under inhomogeneous road conditions, a conserved high-order (CHO) anisotropic traffic flow model was extended to obtain a CHO model with discontinuous fluxes. Based on the property of the Riemann invariant for the CHO model with discontinuous fluxes, the first-order Godunov, EO (Engquist-Osher) and LF (Lax-Friedrichs) numerical schemes for this model were designed with the local simplification method and the δ mapping algorithm. The numerical simulations show that, the CHO model with discontinuous fluxes is reasonable and effective. It can describe equilibrium and non-equilibrium traffic flows, and can better describe the actual traffic phenomena compared with the LWR (Lighthill-Whitham-Richards) model with a discontinuous flux. |
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