Oseen方程的一种新的局部投影稳定化方法

白艳红; 冯民富; 王川龙

doi:10.3879/j.issn.1000-0887.2010.11.009

Oseen方程的一种新的局部投影稳定化方法

doi: 10.3879/j.issn.1000-0887.2010.11.009

太原师范学院数学系, 太原 030012;

基金项目: 国家自然科学基金资助项目(11071184);四川省科技攻关课题资助项目(05GG006-006-2)

详细信息

作者简介:
白艳红(1982- ),女,山西清徐人,博士(E-mail:baiyanhong1982@126.com);冯民富(1964- ),男,教授(联系人.Tel:+86-28-85460879;E-mail:fmf@wtjs.cn).

中图分类号: O241.82
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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-10-05
- 刊出日期: 2010-11-15

A New Nonconforming Local Projection Stabilization for Generalized Oseen Equations

Department of Mathematics, Taiyuan Teachers College, Taiyuan 030012, P. R. China;
Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China

摘要

摘要: 对Oseen方程提出一种新的局部投影稳定化有限元方法,并且速度和压力采用inf-sup稳定的非协调有限元空间逼近．局部投影稳定化项仅加在子网格上(H≥h);与RFB方法相比,该方法稳定性项简单,并且可以克服对流占优．最后,通过实验证明,数值结果和理论结果完全一致．
- Oseen 方程 /
- 局部投影稳定化方法 /
- Crouzeix-Raviart元
Abstract: A new method of nonconforming local projection stabilization for the generalized Oseen equations was proposed by a nonconforming inf-sup stable element pair for approximating the velocity and pressure. The method has several attractive feature. It adds an local projection term only on the sub-scale (H ≥h). The stabilized term is simple compared with the residual-free bubble element method can handle the influence of strong convection. The numerical illustrations agree with the theoretical expectation very well.
- generalized Oseen equations /
- local projection stabilization /
- Crouzeix-Raviart element

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参考文献(15)

[1]	BAI Yan-hong, FENG Min-fu,KONG Hua.Analysis of a nonconforming RFB stabilized method for the nonstationary convection-dominated diffusion equation[J].Mathematica Numerica Sinica, 2009, 31(4): 363-378.
[2]	Franca L P, John V, Matthies G, Tobiska L. An inf-sup stable and residual-free bubble element for the oseen equations[R]. UCDHSC / CCM Report, No. 236, 2007.
[3]	GE Zhi-hao, FENG Min-fu, HE Yin-nian. A stabilized nonconfirming finite element method based on multiscale enrichment for the stationary Navier-Stokes equations[J]. Applied Mathematics and Computation, 2008, 202(2): 700-707. doi: 10.1016/j.amc.2008.03.016
[4]	ZHOU Tian-xiao, FENG Min-fu. A least squares Petrov-Galerkin finite element method for the stationary Navier-Stokes equations[J]. Mathematics of Computation, 1993, 60(202): 531-543. doi: 10.1090/S0025-5718-1993-1164127-6
[5]	Lube G, Rapin G, Lwe G. Local projection stabilization for incompressible flows:equal-order vs. inf-sup stable interpolation[J]. Electronic Transactions on Numerical Analysis, 2008, 32: 106-122.
[6]	骆艳，冯民富. 可压缩Navier-Stokes方程的压力梯度局部投影间断有限元法[J].应用数学和力学, 2008, 29(2): 157-168.
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[8]	Guermond J L, Marra A, Quartapelle L. Subgrid stabilized projection method for 2D unsteady flows at high Reynolds numbers[J]. Computer Methods in Applied Mechanics and Engineering,2006, 195(44/47): 5857-5876. doi: 10.1016/j.cma.2005.08.016
[9]	Hughes T J R, Mazzei L, Jansen K E. Large eddy simulation and the variational multiscale method[J]. Comput Visual Sci, 2000, 3(1/2): 47-59. doi: 10.1007/s007910050051
[10]	Kaya S, Layton W. Subgrid-scale eddy viscosity methods are variational multiscale methods[R]. Pittsburgh, PA: Technical report, TR-MATH 03-05, University of Pittsburgh, 2003.
[11]	John V, Kaya S. Finite element error analysis of a variational multiscale method for the Navier- Stokes equations[J]. Advances in Computational Mathematics, 2008, 28(1): 43-61.
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[13]	Kaya S, RiviIére B. A two-grid stabilization method for solving the steady-state Navier-Stokes equations[J].Numerical Methods for Partial Differential, 2006, 22(3): 728-743. doi: 10.1002/num.20120
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Oseen方程的一种新的局部投影稳定化方法

doi: 10.3879/j.issn.1000-0887.2010.11.009

作者简介:
白艳红(1982- ),女,山西清徐人,博士(E-mail:baiyanhong1982@126.com);冯民富(1964- ),男,教授(联系人.Tel:+86-28-85460879;E-mail:fmf@wtjs.cn).

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A New Nonconforming Local Projection Stabilization for Generalized Oseen Equations

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Oseen方程的一种新的局部投影稳定化方法

doi: 10.3879/j.issn.1000-0887.2010.11.009

作者简介: 白艳红(1982- ),女,山西清徐人,博士(E-mail:baiyanhong1982@126.com);冯民富(1964- ),男,教授(联系人.Tel:+86-28-85460879;E-mail:fmf@wtjs.cn).

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出版历程

A New Nonconforming Local Projection Stabilization for Generalized Oseen Equations

计量

出版历程

目录

作者简介:
白艳红(1982- ),女,山西清徐人,博士(E-mail:baiyanhong1982@126.com);冯民富(1964- ),男,教授(联系人.Tel:+86-28-85460879;E-mail:fmf@wtjs.cn).