强耦合PDE-ODE问题非经典解的保守格式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-01-15 DOI:10.4171/IFB/392

C. Chalons, M. D. Monache, P. Goatin

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引用次数: 31

摘要

我们考虑一个强耦合的PDE-ODE系统，该系统描述了慢速和大型车辆对道路交通的影响。该模型由描述主要交通演变的标量守恒定律和考虑慢速车辆轨迹的ODE组成，该轨迹取决于下游交通密度。移动约束由通量上的一个不等式来操作，这解释了由于慢速车辆的存在而在道路上造成的瓶颈。给出了约束双曲偏微分方程的一种保守格式和一种跟踪算法。给出了数值检验并计算了收敛阶。

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A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem

We consider a strongly coupled PDE-ODE system that describes the influence of a slow and large vehicle on road traffic. The model consists of a scalar conservation law describing the main traffic evolution and an ODE accounting for the trajectory of the slower vehicle that depends on the downstream traffic density. The moving constraint is operated by an inequality on the flux, which accounts for the bottleneck created on the road by the presence of the slower vehicle. We introduce a conservative scheme for the constrained hyperbolic PDE and a tracking algorithm for the ODE. We show numerical tests and compute numerically the order of convergence.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.