留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Navier-Stokes方程的局部投影稳定化方法

覃燕梅 冯民富 罗鲲 吴开腾

覃燕梅, 冯民富, 罗鲲, 吴开腾. Navier-Stokes方程的局部投影稳定化方法[J]. 应用数学和力学, 2010, 31(5): 618-630. doi: 10.3879/j.issn.1000-0887.2010.05.013
引用本文: 覃燕梅, 冯民富, 罗鲲, 吴开腾. Navier-Stokes方程的局部投影稳定化方法[J]. 应用数学和力学, 2010, 31(5): 618-630. doi: 10.3879/j.issn.1000-0887.2010.05.013
QIN Yan-mei, FENG Min-fu, LUO Kun, WU Kai-teng. Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(5): 618-630. doi: 10.3879/j.issn.1000-0887.2010.05.013
Citation: QIN Yan-mei, FENG Min-fu, LUO Kun, WU Kai-teng. Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(5): 618-630. doi: 10.3879/j.issn.1000-0887.2010.05.013

Navier-Stokes方程的局部投影稳定化方法

doi: 10.3879/j.issn.1000-0887.2010.05.013
基金项目: 国家自然科学基金资助项目(10872085);四川省科技攻关课题资助项目(05GG006-006-2);内江师范学校青年科研项目(09NJZ-6)的资助
详细信息
    作者简介:

    覃燕梅(1980- ),女,四川青神人,讲师,硕士(联系人.Tel:+86-832-5063638;E-mail:qinyanmei0809@163.com);冯民富(1964- ),男,四川人,教授,博士(E-mail:fmf@wtjs.cn).

  • 中图分类号: O242.21

Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations

  • 摘要: 将Matthies,Skrzypacz和Tubiska的思想从线性的Oseen方程拓展到了非线性的Navier-Stokes方程,针对不可压缩的定常Navier-Stokes方程,提出了一种局部投影稳定化有限元方法.该方法既克服了对流占优,又绕开了inf-sup条件的限制.给出的局部投影空间既可以定义在两种不同网格上,又可以定义在相同网格上.与其他两级方法相比,定义在同一网格空间上的局部投影稳定化格式更紧凑.在同一网格上,除了给出需要bubble函数来增强的逼近空间外,还特别考虑了两种不需要用bubble函数来增强的新的空间.基于一种特殊的插值技巧,给出了稳定性分析和误差估计.最后,还列举了两个数值算例,进一步验证了理论结果的正确性.
  • [1] Franca L P, Frey S L. Stabilized finite element methods: Ⅱ.The incompressible Navier-Stokes equations[J].Comput Methods Appl Mech Eng, 1992, 99(2/3):209-233. doi: 10.1016/0045-7825(92)90041-H
    [2] Tobiska L, Verfürth R. Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equation[J]. SIAM J Numer Anal, 1996, 33(1):107-127. doi: 10.1137/0733007
    [3] Li J, He Y N, Chen Z X. Performance of several stabilized finite element methods for the Stokes equations based on the lowest equal-order pairs[J]. Computing, 2009, 86(1):37-51. doi: 10.1007/s00607-009-0064-5
    [4] He Y N, Li J. A stabilized finite element method based on local polynomial pressure projection for the stationary Navier-Stokes equations[J]. Applied Numerical Mathematics, 2008, 58(10):1503-1514. doi: 10.1016/j.apnum.2007.08.005
    [5] Li J, He Y N, Xu H. A multi-level stabilized finite element method for the stationary Navier-Stokes equations[J]. Comput Methods Appl Mech Eng, 2007, 196(4/6):2852-2862. doi: 10.1016/j.cma.2006.12.007
    [6] Li J, He Y N, Chen Z X. A new stabilized FEM for the transient Navier-Stokes equations[J]. Comput Methods Appl Mech Engng,2007, 197(1/4):22-35. doi: 10.1016/j.cma.2007.06.029
    [7] 覃燕梅,冯民富,周天孝. 瞬态Navier-Stokes方程的一种新的全离散粘性稳定化方程[J].应用数学和力学,2009, 30(7):783-778.
    [8] 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.
    [9] 罗琨,冯民富,王成. 一个精确的免闭锁四边形板元[J].四川大学学报(工程科学版), 2006, 38(1):44-48.
    [10] Becker R, Braack M. A finite element pressure gradient stabilization for the Stokes equations based on local projections[J].Calcolo, 2001, 38(4):173-199. doi: 10.1007/s10092-001-8180-4
    [11] Becker R, Braack M. A two-level stabilization scheme for the Navier-Stokes equations[C]Feistauer M, Doleji V, Knobloch P, et al.Numerical Mathematics and Advanced Applications,Berlin: Springer-Verlag, 2003, 123-130.
    [12] Braack M, Burman E. Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method[J]. SIAM J Numer Anal, 2006, 43(6):2544-2566. doi: 10.1137/050631227
    [13] Matthies G, Skrzypacz P, Tobiska L. A unified converagence analysis for local projection stabilisations applied to the Oseen problem[J]. Mathematical Modelling and Numerical Analysis, 2007, 41(4).
    [14] Codina R, Blasco J. Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations[J]. Numer Math, 2000,87(1):59-81. doi: 10.1007/s002110000174
    [15] Codina R, Blasco J. A finite element formulation for the Stokes problem allowing equal velocity-ressure interpolation[J]. Comput Meth Appl Mech Engng, 1997, 143(3/4):373-391. doi: 10.1016/S0045-7825(96)01154-1
    [16] Codina R, Blasco J. Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient projection[J]. Comput Methods Appl Mech Engng, 2000, 182(3/4):277-300. doi: 10.1016/S0045-7825(99)00194-2
    [17] Codina R,Vzquez M, Zienkiewicz O C. A general algorithm for compressible and incompressible follow—part Ⅲ: the semiimplicit form[J]. Int J Numer Meth Fluids, 1998, 27(1/4):13-32. doi: 10.1002/(SICI)1097-0363(199801)27:1/4<13::AID-FLD647>3.0.CO;2-8
    [18] Chacn T. A term by term stabilization algorithm for the finite element solution of incompressible flow problems[J]. Numerische Mathematik, 1998, 79(2):283-319. doi: 10.1007/s002110050341
    [19] Franca L P, Frey S L. Stabilized finite element methods: II.The incompressible Navier-Stokes equations[J]. Comput Methods Appl Mech Eng, 1992, 99(2/3):209-233. doi: 10.1016/0045-7825(92)90041-H
    [20] Tobiska L, Lube G. A modified streamline-diffusion method for solving the stationary Navier-Stokes equations[J]. Numerische Mathematik, 1991, 59(1):13-29. doi: 10.1007/BF01385768
    [21] Tobiska L, Verfrth R. Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations[J]. SIAM J.Numerical Analy, 1996, 33(1):107-127. doi: 10.1137/0733007
    [22] Girault V, Raviart P. Finite Element Methods for the Navier-Stokes Equations[M].Berlin:Springer, 1986.
  • 加载中
计量
  • 文章访问数:  1195
  • HTML全文浏览量:  36
  • PDF下载量:  764
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-10-26
  • 修回日期:  2010-03-22
  • 刊出日期:  2010-05-15

目录

    /

    返回文章
    返回