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
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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

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

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参考文献(20)

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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).

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

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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).