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  

A EXTRAPOLATION REDUCED-ORDER FDS BASED ON POD TECHNIQUE FOR TRAFFIC FLOW MODEL

作　　者：罗振东[1] 高骏强[1] 孙萍[2] 安静[2] 

机构地区：[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

出　　处：《计算数学》2013年第2期159-170,共12页Mathematica Numerica Sinica

基　　金：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;河北省自然科学基金(批准号:A2010001 663)

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.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.

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 

分 类 号：O241.82[理学—计算数学]