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求解Oseen流的交替线松弛多重网格方法

朱兴文 张立翔

朱兴文, 张立翔. 求解Oseen流的交替线松弛多重网格方法[J]. 应用数学和力学, 2016, 37(11): 1145-1155. doi: 10.21656/1000-0887.370062
引用本文: 朱兴文, 张立翔. 求解Oseen流的交替线松弛多重网格方法[J]. 应用数学和力学, 2016, 37(11): 1145-1155. doi: 10.21656/1000-0887.370062
ZHU Xing-wen, ZHANG Li-xiang. Solution of the Oseen Flow With the Multigrid Method Based on Alternating-Line Relaxation[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1145-1155. doi: 10.21656/1000-0887.370062
Citation: ZHU Xing-wen, ZHANG Li-xiang. Solution of the Oseen Flow With the Multigrid Method Based on Alternating-Line Relaxation[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1145-1155. doi: 10.21656/1000-0887.370062

求解Oseen流的交替线松弛多重网格方法

doi: 10.21656/1000-0887.370062
基金项目: 国家自然科学基金(51279071);教育部博士点基金(优先)资助项目(20135314130002)
详细信息
    作者简介:

    朱兴文(1985—),男,讲师,博士生(E-mail: zxw4688@126.com);张立翔(1959—),男,教授,博士生导师(通讯作者. E-mail: zlxzcc@126.com).

  • 中图分类号: O241.8;O241.1;O241.6

Solution of the Oseen Flow With the Multigrid Method Based on Alternating-Line Relaxation

Funds: The National Natural Science Foundation of China(51279071)
  • 摘要: 利用Riemann解的通量差分分裂法——Godunov方法对Oseen流控制方程进行离散,得到了基于一阶上迎风格式的离散方程,并给出了使用多重网格方法求解该离散方程的V循环算法和W-循环算法的收敛性分析.通过局部Fourier分析方法,对获得的离散方程的聚对称交替线Gauss-Seidel松弛的光滑性质进行了研究.结果表明:使用多重网格的两层网格及三层网格算法求解具有不同Reynolds数的Oseen流,即便是在高Reynolds数情况下,聚对称交替线Gauss-Seidel松弛具有很好的光滑性质,多重网格W-循环算法收敛性比V-循环算法好.
  • [1] Temam R.Navier-Stokes Equations: Theory and Numerical Analysis[M]. Rhode Island: American Mathematic Society, 2001.
    [2] Trottenberg U, Oosterlee C W, Schüller A.Multigrid[M]. New York: Academic Press, 2001.
    [3] Wienands R, Joppich W.Practical Fourier Analysis for Multigrid Methods[M]. Boca Raton, FL: Chapman and Hall/CRC Press, 2005.
    [4] Briggs W L, Henson V E, McCormick S.A Multigrid Tutorial[M]. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2000.
    [5] Hackbusch W.Multi-Grid Methods and Applications[M]. Berlin: Springer, 1985.
    [6] Wesseling P.An Introduction to Multigrid Methods[M]. Chichester, UK: John Wiley, 1992.
    [7] Stuben K, Trottenberg U.Multigrid Methods: Fundamental Algorithms, Model Problem Analysis and Applications[M]. Hackbusch W, Trottenberg U, ed.Lectwe Notes in Mathematics,Vol960. Berlin: Springer-Verlag, 1982: 1-176.
    [8] Brandt A, Livne O E.Multigrid Techniques: 1984 Guide With Applications to Fluid Dynamics[M]. Revised, ed. Society for Industrial and Applied Mathematics, 2011.
    [9] Roe P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J].Journal of Computational Physics,1997,135(2): 250-258.
    [10] Osher S, Chakravarthy S. Upwind schemes and boundary conditions with applications to Euler equations in general geometries[J].Journal of Computational Physics,1983,50(3): 447-481.
    [11] Einfeldt B, Munz C D, Roe P L, Sjgreen B. On Godunov-type methods near low densities[J].Journal of Computational Physics,1991,92(2): 273-295.
    [12] Abdullah S, LI Yuan, Aftab K. Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations[J].Applied Mathematics and Computation,2010,215(9): 3201-3213.
    [13] Toro E F.Riemann Solvers and Numerical Methods for Fluid Dynamics[M]. 2nd ed. Berlin: Springer-Verlag, 2009.
    [14] Oosterlee C W, Lorenz F J G. Multigrid methods for the Stokes system[J].Computing in Science & Engineering,2006:8(6): 34-43.
    [15] Wittum G. Multi-grid methods for Stokes and Navier-Stokes equations[J].Numerische Mathematic,1989,54(5): 543-563.
    [16] WANG Ming, CHEN Long. Multigrid methods for the Stokes equations using distributive Gauss-Seidel relaxations based on the least squares commutator[J].Journal of Scientific Computing,2013,56(2): 409-431.
    [17] ur Rehman M, Geenen T, Vuik C, Segal G, MacLachlan S P. On iterative methods for the incompressible Stokes problem[J].International Journal for Numerical Methods in Fluids,2011,65(10): 1180-1200.
    [18] Bacuta C, Vassilevski P S, ZHANG Shang-you. A new approach for solving Stokes systems arising from a distributive relaxation method[J].Numerical Methods for Partial Differential Equations,2011,27(4): 898-914.
    [19] Wienands R, Gaspar F J, Lisbona F J, Oosterlee C W. An efficient multigrid solver based on distributive smoothing for poroelasticity equations[J].Computing,2004,73(2): 99-119.
    [20] Pillwein V, Takacs S. A local Fourier convergence analysis of a multigrid method using symbolic computation[J].Journal of Symbolic Computation,2014,63: 1-20.
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出版历程
  • 收稿日期:  2016-03-03
  • 修回日期:  2016-04-25
  • 刊出日期:  2016-11-15

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