计算数学
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计算数学  2013, Vol. 35 Issue (2): 159-170    DOI:
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交通流模型基于特征投影分解技术的外推降维有限差分格式
罗振东1, 高骏强1, 孙萍2, 安静2
1. 华北电力大学数理学院, 北京 102206;
2. 贵州师范大学数学与计算机科学学院, 贵阳 550001
A EXTRAPOLATION REDUCED-ORDER FDS BASED ON POD TECHNIQUE FOR TRAFFIC FLOW MODEL
Luo Zhendong1, Gao Junqiang1, Sun Ping2, An Jing2
1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;
2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China
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摘要 利用特征正交分解(proper orthogonal decomposition,简记为POD)技术研究交通流的Aw-Rascle-Zhang(ARZ)模型. 建立一种基于 POD方法维数较低的外推降维有限差分格式, 并用数值例子检验数值计算结果与理论结果相吻合, 进一步表明基于POD方法的外推降维有限差分格式对于求解交通流方程数值解是可行和有效的.
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关键词特征正交分解   交通流ARZ模型   外推降维有限差分格式   数值模拟     
Abstract: In this paper, a traffic flow Aw-Rascle-Zhang(ARZ) model is studied with a proper orthogonal decomposition (POD) technique. A extrapolation reduced-order finite difference scheme (FDS) based on POD method with lower dimension is established. And a numerical example is used to verify that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the extrapolation reduced-order FDS based on POD method is feasible and efficient for finding numerical solutions for traffic flow equation.
Key wordsproper orthogonal decomposition   traffic flow ARZ model   extrapolation reduced-order finite difference scheme   numerical simulation   
收稿日期: 2012-07-16;
基金资助:

国家自然科学基金(批准号: 11271127和11061009)、贵州省科技计划课题(批准号: 黔科合J字[2011]2367)和河北省自然科学基金(批准号:A2010001663).

引用本文:   
. 交通流模型基于特征投影分解技术的外推降维有限差分格式[J]. 计算数学, 2013, 35(2): 159-170.
. A EXTRAPOLATION REDUCED-ORDER FDS BASED ON POD TECHNIQUE FOR TRAFFIC FLOW MODEL[J]. Mathematica Numerica Sinica, 2013, 35(2): 159-170.
 
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