求解Oseen流的交替线松弛多重网格方法

朱兴文; 张立翔

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

朱兴文^1,2,
张立翔¹

¹昆明理工大学工程力学系, 昆明 650500;²大理大学数学与计算机学院, 云南大理 671003

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
计量
- 文章访问数: 755
- HTML全文浏览量: 71
- PDF下载量: 513
- 被引次数: 0
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

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

ZHU Xing-wen^1,2,
ZHANG Li-xiang¹

¹Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming 650500, P.R.China;¹School of Mathematics and Computer, Dali University, Dali, Yunnan 671003, P.R.China

Funds: The National Natural Science Foundation of China(51279071)

摘要

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.
- 通量差分分裂法 /
- 多重网格方法 /
- Oseen流 /
- 局部Fourier分析 /
- 交替线松弛
Abstract: The 1st-order upwind discretization form of the Oseen flow was obtained through the Godunov-type flux-difference splitting approach based on the Riemann solver. The convergence analysis of 2 kinds of cycling algorithms, i.e., the V-cycle and the W-cycle in the multigrid method for the solution of the discretized equations, was performed. Furthermore, the smooth properties of the collective symmetrical alternating-line Gauss-Seidel relaxation was investigated by means of the local Fourier analysis. The numerical results show that the collective symmetrical alternating-line Gauss-Seidel relaxation has sound smooth properties, and the convergence of the W-cycle algorithm is better than that of the V-cycle one in the multigrid method for the solution of the Oseen flow with different Reynolds numbers.
- flux-difference splitting /
- multigrid method /
- Oseen flow /
- local Fourier analysis /
- alternating-line relaxation

HTML全文

参考文献(20)

[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.

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 755
HTML全文浏览量: 71
PDF下载量: 513
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

求解Oseen流的交替线松弛多重网格方法

doi: 10.21656/1000-0887.370062

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).

计量

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

计量

目录

留言板

求解Oseen流的交替线松弛多重网格方法

doi: 10.21656/1000-0887.370062

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).

计量

出版历程

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

计量

出版历程

目录

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).