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非定常线性化Navier-Stokes方程的子格粘性非协调有限元方法

孔花1, 冯民富2, 覃燕梅3   

  1. 1. 内江师范学院, 数学与信息科学学院/四川省高等学校数值仿真重点实验室, 四川内江, 641112;
    2. 四川大学数学学院, 成都 610064;
    3. 数学与信息科学学院/四川省高等学校数值仿真重点实验室, 四川内江, 641112
  • 收稿日期:2012-09-20 出版日期:2013-02-15 发布日期:2013-01-22
  • 通讯作者: 覃艳梅(1980-), 女, 四川青神人, 副教授.E-mail:qinyanmei0809@163.com.
  • 基金资助:

    国家自然科学基金项目(编号:11271273),四川省教育厅青年基金项目(编号:11ZB175)资助.

孔花, 冯民富, 覃燕梅. 非定常线性化Navier-Stokes方程的子格粘性非协调有限元方法[J]. 计算数学, 2013, 35(1): 99-112.

Kong Hua, Feng Minfu, Qin Yanmei. A NON-CONFORMING FINITE ELEMENT METHOD OF SUBGRID VISCOSITY METHOD FOR THE NON-STATIONARY LINEARIZED NAVIER-STOKES EQUATIONS[J]. Mathematica Numerica Sinica, 2013, 35(1): 99-112.

A NON-CONFORMING FINITE ELEMENT METHOD OF SUBGRID VISCOSITY METHOD FOR THE NON-STATIONARY LINEARIZED NAVIER-STOKES EQUATIONS

Kong Hua1, Feng Minfu2, Qin Yanmei3   

  1. 1. Colledge of Mathematics and Information Sciences/Key Laboratory of Numberical Simulation of Sichuan Province, Neijiang Normal University, Neijiang 641112, Sichuan, China;
    2. College of Mathematics, Sichuan University, Chengdu 610064, China;
    3. Colledge of Mathematics and Information Sciences/Key Laboratory of Numberical Simulation of Sichuan Province, Neijiang Normal University, Neijiang 641112, Sichuan, China
  • Received:2012-09-20 Online:2013-02-15 Published:2013-01-22
本文结合子格粘性法的思想,空间采用非协调Crouzeix-Raviart元逼近,时间采用Crank-Nicolson差分离散,对非定常线性化Navier-Stokes方程建立了全离散的子格粘性非协调有限元格式.对稳定性和误差估计作出了详细的分析, 得出了最优的误差估计.最后, 通过数值算例进一步验证了该方法的稳定性和收敛性.
For the non-stationary linearized Navier-Stokes equations, a non-conforming finite element method of subgrid viscosity method is presented, where Crouzeix-Raviart nonconforming finite element is employed, and the Crank-Nicholson scheme is used for time discretization. Stability and convergence of the method is proved. The error estimation results show that the method achieves optimal accuracy with respect to solution regularity. The numerical results were given, which demonstrate the stability and convergence of the method presented.

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[1] Girault V, Raviart P A. Finite element approximation of the Navier-Stokes equations[M]. BerlinHeidelberg New York: Springer, 1979.

[2] Brooks A N and Hughes T J R. Streamline upwind/Petrov-Galerkin formulations for convectiondomainated flows with particular emphasison the incompreesible Navier-Stokes equations[J].Comput. Mrthods Appl. Mech. Eng., 1982, 32: 199-259.

[3] Sun C and Shen H. FDSD method for timedependent convection-diffusion equations[J]. Numer.Math., A Journal of Chinese Universities, English Series, 1998, 7: 72-85.

[4] Layton W. A connection between subgrid scale eddy viscosity and mixed methods[J]. J. Appl.Math. Comput., 2002, 133: 147-157.

[5] John V, Maubach J M and Tobiska L. Nonconforming streamline-diffusion finite element methodsfor convection-diffusion problems[J]. Numer. Math., 1997, 78: 165-188.

[6] John V, Matthies G, Schieweck F and Tobiska L. A streamline-diffusion method for nonconformingfinite element approximations applied to convection-diffusion problems[J]. Comput. Methods Appl.Mech. Engrg., 1998, 166: 85-97.

[7] Knobloch P and Tobiska L. A streamline-diffusion method for nonconforming finite element approximatonsapplied to the linearized incompressible Navier-Stokes equations[R]. World Scientific,Singapore, 1999: 530- 538.

[8] Chen Y M and Xie X P. A streamline diffusion nonconforming finite element method for thetime-dependent linearized Navier-Stokes equations[J]. Appl. Math. Mech, 2010, 31(7): 861-874.

[9] Smagorinsky J. General circulation experiments with the primitive equaltion[J]. Monthly WeatherRewview, 1963, 91 : 99-164.

[10] Guermond J L. Stabilization of Galerkin approximations of transport equations by subgrid modelling[J]. MA2N, 1999, 33: 1293-1316.

[11] Layton W. A connection between subgrid scale eddy viscosity and mixed methods[J]. AppliedMathematics and Computation, 2002, 133: 147-157.

[12] Kaya S. Numerical analysiss of a subgrid scale eddy viscosity method for hiegher Reynolds numberflow problem[R]. Technical report : University of Pittsburgh, 2003.

[13] Hughes T J R. Multiscale phenomena: Green's functions, the Dirichletto-Neumann formulation,subgrid-scale models, bubbles and the origin of stabilized methods[J]. Comput. Mrthods Appl.Mech. Eng., 1995, 127: 387-401.

[14] Hughes T J R, Mazzei L and Jansen K E. Large eddy simulation and the variational multiscalemethod[J]. Comput Visual Sci, 2000(3) : 47-59.

[15] Kaya S, Latyon W J. Subgrid-scale viscosity methds are variational multiscale methods[R]. Technicalreport : University of Pittsburgh, 2003.

[16] Alaoui L E and Ern A. Nonconforming finite element methods with subgrid viscosity applied toadvection-diffusive-reaction equations[J]. Numerical Methods for Partial Differential Equations,2006, 22(5) : 1106-1126.

[17] Bai Y H, Feng M F, Wang C H. Nonconforming local projection stabilization for generalized Oseenequations[J]. J. Appl. Math. Comput., 2010, 31(11) : 1360-1371.

[18] 常晓蓉, 冯民富. 非定常对流扩散问题的非协调局部投影有限元方法[J].计算数学, 2011, 33(3): 275-288.

[19] Kaya S, Riviere B. A two-grid method for solving the steady-state Navier-Stokes equatioins,Numer.Meth.Part.D.E., 2006, 22:728-743.

[20] Qin Y M, Feng M F, Zhou X T. A new full discrete stabilized viscosity method for transientNavier-Stokes equations[J]. J. Appl. Math. Comput., 2009, 30(7):839-852.

[21] Feng M F, Bai Y H, He Y N, e.t. A new stabilized subgrid eddy viscosity method based on pressureprojection and extrapolated trapezoidal rule for the transient Navier- Stokes equations[J]. Journalof Computational Mathematics, 2011, 29(4):415-440.

[22] 白艳红, 冯民富, 孔花. 非定常对流占优扩散方程的非协调RFB稳定化方法分析[J]. 计算数学, 2009, 31(4) :363-378.
[1] 白艳红, 冯民富, 孔花. 非定常对流占优扩散方程的非协调RFB稳定化方法分析[J]. 计算数学, 2009, 31(4): 363-378.
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