Efficient implementation of the shock‐fitting algorithm for the Lighthill–Whitham–Richards traffic flow model
Efficient implementation of the shock‐fitting algorithm for the Lighthill–Whitham–Richards traffic flow model
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DOI：
10.1002/nme.2185
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发表时间：
2008-04
影响因子：
2.9
通讯作者：
Wenqin Chen;S. Wong;Chi-Wang Shu
中科院分区：
文献类型：
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作者：
Wenqin Chen;S. Wong;Chi-Wang Shu
本文首先根据交通流密度沿着激波变化的单调性，给出了求解线性速度-密度关系的Lighthill-Whitham-理查兹（LWR）交通流模型的解析激波拟合算法中相邻激波或激波与特征线相交时间的存在唯一性，这大大提高了分析冲击拟合算法的鲁棒性。然后，我们讨论了有效性的措施（莫伊）的分析冲击拟合算法的有效性评估。我们开发了显式表达式来计算MOE，MOE是旅行者在由冲击和/或特征线所包围的时空区域内所产生的总旅行时间。数值算例表明，该方法与五阶加权基本无振荡格式的数值解相比，具有较高的计算效率和有效性.版权所有© 2007约翰威利父子有限公司。
This paper firstly presents the existence and uniqueness properties of the intersection time between two neighboring shocks or between a shock and a characteristic for the analytical shock‐fitting algorithm that was proposed to solve the Lighthill–Whitham–Richards (LWR) traffic flow model with a linear speed–density relationship in accordance with the monotonicity properties of density variations along a shock, which have greatly improved the robustness of the analytical shock‐fitting algorithm. Then we discuss the efficient evaluation of the measure of effectiveness (MOE) of the analytical shock‐fitting algorithm. We develop explicit expressions to calculate the MOE–which is the total travel time that is incurred by travelers, within the space‐time region that is encompassed by the shocks and/or characteristic lines. A numerical example is used to illustrate the effectiveness and efficiency of the proposed method compared with the numerical solutions that are obtained by a fifth‐order weighted essentially non‐oscillatory scheme. Copyright © 2007 John Wiley & Sons, Ltd.