非定常Stokes方程一种基于POD方法的简化有限差分格式

罗振东; 欧秋兰; 谢正辉

doi:10.3879/j.issn.1000-0887.2011.07.004

非定常Stokes方程一种基于POD方法的简化有限差分格式

doi: 10.3879/j.issn.1000-0887.2011.07.004

1.
华北电力大学数理学院,北京 102206;
中国科学院大气物理研究所,北京 100029

基金项目: 国家自然科学基金资助项目(10871022;11061009;40821092);国家973资助项目(2010CB428403;2009CB421407;2010CB951001);河北省自然科学基金资助项目(A2010001663)

详细信息

作者简介:
罗振东(1958- ),男,广西人,教授,博士,博士生导师(联系人.E-mai:lzhdluo@163.com)

中图分类号: O241.82
计量
- 文章访问数: 1891
- HTML全文浏览量: 206
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- 被引次数: 0
出版历程
- 收稿日期: 2011-03-24
- 修回日期: 2011-04-25
- 刊出日期: 2011-07-15

A Reduced Finite Difference Scheme and Error Estimates Based on POD Method for the Non-Stationary Stokes Equation

1.
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China;
ICCES/LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, P. R. China

摘要

摘要: 特征正交分解(proper orthogonal decomposition,简记为POD)方法是一种可对偏微分方程的物理模型(如流体流动)做简化的技术．这种方法已经成功地用于对复杂系统模型降阶．推广应用POD方法,将POD方法应用于具有实际应用背景的非定常Stokes方程经典的有限差分格式,建立一种维数较低而精度足够高的简化差分格式,并给出简化差分格式解与经典差分格式解的误差估计．数值例子说明数值计算结果与理论结果相吻合．进一步表明基于POD方法的简化差分格式对求解非定常Stokes方程数值解是可行和有效的．
- 有限差分格式 /
- 特征正交分解 /
- 误差估计 /
- 非定常Stokes方程
Abstract: The properorthogonal decom position (POD) was amodel reduction technique for the simulation of physical processes governed by partial differen tial equations, e. g. fluid flows. It was success fully used in the reduced-ordermodeling of complex systems. The applications of POD method were extended, i. e., apply POD method to a classical finited ifference (FD) scheme for the non-stationary Stokes equation with real practical applied background, estab lish a reduced FD scheme with lowerd imensions and sufficiently high accuracy, and provide the errorestmi ates between the reduced FD solutions and the classical FD solutions. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD schemebased on POD method is feasible and efficient for solving FD scheme for the non-stationary Stokes equation.
- finite difference scheme /
- proper orthogonal decomposition /
- error estimate /
- non-stationary Stokes equation

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参考文献(30)

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