非定常Stokes方程的降阶稳定化CN有限体积元外推模型

腾飞; 罗振东

doi:10.3879/j.issn.1000-0887.2014.09.005

非定常Stokes方程的降阶稳定化CN有限体积元外推模型

doi: 10.3879/j.issn.1000-0887.2014.09.005

腾飞¹,
罗振东²

¹凯里学院数学科学学院, 贵州凯里 556011;²华北电力大学数理学院, 北京102206

基金项目: 国家自然科学基金(11271127)；贵州省教育厅自然科学研究项目(黔教合KY字[2013]207)

详细信息

作者简介:
腾飞(1986—), 女, 吉林人, 讲师, 硕士(E-mail: tengfeikl@126.com);罗振东(1958—), 男, 广西桂平人, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

中图分类号: O242.21
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出版历程
- 收稿日期: 2014-05-15
- 修回日期: 2014-06-06
- 刊出日期: 2014-09-15

A Reduced-Order Stabilized CNFVE Extrapolating Model for Non-Stationary Stokes Equations

TENG Fei¹,
LUO Zhen-dong²

¹School of Mathematical Science, Kaili University, Kaili, Guizhou 556011, P.R.China;²School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R.China

Funds: The National Natural Science Foundation of China(11271127)

摘要

摘要: 利用稳定化的Crank-Nicolson(CN)有限体积元方法和特征投影分解方法，建立非定常Stokes方程的一种自由度很少、精度足够高的降阶稳定化CN有限体积元外推模型,并给出这种降阶稳定化CN有限体积元外推模型解的误差估计和算法的实现.最后用数值例子说明数值结果与理论结果相吻合,并阐明这种降阶稳定化CN有限体积元外推模型的优越性.
- 稳定化CN有限体积元方法 /
- 特征投影分解方法 /
- 非定常Stokes方程 /
- 误差估计
Abstract: A reduced-order stabilized Crank-Nicolson finite volume element (SCNFVE) extrapolating model with sufficiently high accuracy and few degrees of freedom for non-stationary Stokes equations was established by means of the SCNFVE method and the proper orthogonal decompostion (POD) technique. The error estimates of the reduced-order approximate solutions and the algorithm implementation for the reduced-order SCNFVE extrapolating model were provided. Finally, a numerical example of conduit flow indicates that the results of the proposed model are consistent with those of the theoretical solution. Moreover, the advantages of lower computation complexity and higher calculation accuracy of the reduced-order SCNFVE extrapolating model are shown in comparison with the classical methods.
- stabilized Crank-Nicolson finite volume element method /
- proper orthogonal decomposition method /
- non-stationary Stokes equation /
- error estimate

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参考文献(18)

[1]	Chung T.Computational Fluid Dynamics[M]. Cambridge: Cambridge University Press, 2002.
[2]	Ye X. On the relationship between finite volume and finite element methods applied to the Stokes equations[J].Numerical Methods for Partial Differential Equation,2001,17: 440-453.
[3]	Yang M, Song H L. A postprocessing finite volume method for time-dependent Stokes equations[J].Applied Numerical Mathematics,2009, 59(8): 1922-1932.
[4]	Li R H, Chen Z Y, Wu W.Generalized Difference Methods for Differential Equations-Numerical Analysis of Finite Volume Methods[M]. New York: Marcel Dekker Inc, 2000.
[5]	An J, Sun P, Luo Z D, Huang X. A stabilized fully discrete finite volume element formulation for non-stationary Stokes equation[J].Mathematica Numerica Sinica,2011,33(2): 213-224.
[6]	Holmes P, Lumley J L, Berkooz G.Turbulence, Coherent Structures, Dynamical Systems and Symmetry [M]. Cambridge: Cambridge University Press, 1996.
[7]	Fukunaga K.Introduction to Statistical Recognition[M]. New York: Academic Press, 1990.
[8]	Jolliffe I T.Principal Component Analysis[M]. Berlin: Springer-Verlag, 2002.
[9]	Selten F. Baroclinic empirical orthogonal functions as basis functions in an atmospheric model [J].J Atmosph Sci,1997,54: 2099-2114.
[10]	Sirovich L. Turbulence and the dynamics of coherent structures: part I—III [J]. Quarterly of Applied Mathematics, 1987,45: 561-590.
[11]	Luo Z D, Xie Z H, Shang Y Q, Chen J. A reduced finite volume element formulation and numerical simulations based on POD for parabolic equations[J].Journal of Computational and Applied Mathematics,2011,235(8): 2098-2111.
[12]	Luo Z D, Li H, Zhou Y J, Huang X. A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem[J].Journal of Mathematical Analysis and Applications,2012,385: 310-321.
[13]	Luo Z D, Li H, Chen J. A reduced-order finite volume element formulation based on POD method and implementation of its extrapolation algorithm for unsaturated soil water flow equation (in Chinese)[J]. Sci Sin Math,2012,42(12): 1263-1280.
[14]	Luo Z D, Li H, Sun P, An J, Navon I M. A reduced finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems[J].Mathematics and Computers in Simulation,2013,89: 50-68.
[15]	Adams R A. Sobolev Spaces[M]. New York: Academic Press, 1975.
[16]	罗振东. 混合有限元法基础及其应用[M]. 北京: 科学出版社, 2006.(LUO Zheng-dong. The Foundations and Applications of Mixed Finite Element Methods[M]. Beijing: Science Press, 2006.(in Chinese))
[17]	Temam R. Navier-Stokes Equations[M]. 3rd ed. New York, Amesterdam, 1984.
[18]	Rudin W. Functional and Analysis[M]. 2nd ed. New York: McGraw-Hill Companies, Inc， 1973.

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非定常Stokes方程的降阶稳定化CN有限体积元外推模型

doi: 10.3879/j.issn.1000-0887.2014.09.005

作者简介:
腾飞(1986—), 女, 吉林人, 讲师, 硕士(E-mail: tengfeikl@126.com);罗振东(1958—), 男, 广西桂平人, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

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A Reduced-Order Stabilized CNFVE Extrapolating Model for Non-Stationary Stokes Equations

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非定常Stokes方程的降阶稳定化CN有限体积元外推模型

doi: 10.3879/j.issn.1000-0887.2014.09.005

作者简介: 腾飞(1986—), 女, 吉林人, 讲师, 硕士(E-mail: tengfeikl@126.com);罗振东(1958—), 男, 广西桂平人, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

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出版历程

A Reduced-Order Stabilized CNFVE Extrapolating Model for Non-Stationary Stokes Equations

计量

出版历程

目录

作者简介:
腾飞(1986—), 女, 吉林人, 讲师, 硕士(E-mail: tengfeikl@126.com);罗振东(1958—), 男, 广西桂平人, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).