用稳定双共轭梯度方法数值求解球坐标系下的Poisson方程

doi:10.3969/j.issn.0253-2778.2017.08.009

中国科学技术大学学报 ›› 2017, Vol. 47 ›› Issue (8): 695-698.DOI: 10.3969/j.issn.0253-2778.2017.08.009

用稳定双共轭梯度方法数值求解球坐标系下的Poisson方程

魏安华，吴茜茜，朱祚金

1.中国科学技术大学计算机科学与技术学院，安徽合肥 230027; 2.合肥工业大学数学学院，安徽合肥 230009；
3.中国科学技术大学工程科学学院，安徽合肥 230027

收稿日期:2015-11-11 修回日期:2016-03-24 出版日期:2017-08-31 发布日期:2017-08-31
通讯作者: 朱祚金
作者简介:魏安华，男，1955 年生，硕士/讲师，研究方向：计算机应用. E-mail: weianhua@ustc.edu.cn
基金资助:
国家自然科学基金(11372303)资助.

Numerical solution to the Poisson equation under the spherical coordinate system with Bi-CGSTAB method

WEI Anhua, WU Qianqian, ZHU Zuojin*

1. School of Computer Science and Technology, University of Science and Technology of China， Hefei 230027, China;
2. School of Mathematics, Hefei University of Technology， Hefei 230009, China；
3. School of Engineering Science，University of Science and Technology of China， Hefei 230027, China

Received:2015-11-11 Revised:2016-03-24 Online:2017-08-31 Published:2017-08-31

摘要/Abstract

摘要： 数值求解球坐标系下的Poisson方程，是计算流体力学的一个关键问题.为此提出用稳定双共轭梯度方法，求解了右端源项为-1、边界值为0 的典型Poisson方程，给出了类似于圆射流计算区域Ω:{r∈[7,52], θ∈[-θb,θb], φ∈[0,2π]， θb=arctan(1/14)}内的数值解，并对数值解及其离散方程的残差进行了讨论.

关键词: Bi-CGSTAB(稳定双共轭梯度方法), Poisson方程, 离散方程残差

Abstract: Solving the Poisson equations in spherical coordinate system is a key problem in computational fluid dynamics. Hence, using a conjugate gradient method named Bi-CGSTAB, the typical Poisson equation whose right-hand-side source term is-1 with zero boundary value was solved to give a numerical solution in a domain similar to that in round jet calculation Ω:{ r∈[7,52],  θ∈[-θb,θb], φ∈ [0,2π], θb=arctan(1/14)}. The numerical solution and its relevant residual of discretized equation were discussed.

Key words: Bi-CGSTAB, Poisson equation, residual of discretized equation

中图分类号:

O241.8

魏安华，吴茜茜，朱祚金. 用稳定双共轭梯度方法数值求解球坐标系下的Poisson方程[J]. 中国科学技术大学学报, 2017, 47(8): 695-698.

WEI Anhua, WU Qianqian, ZHU Zuojin*. Numerical solution to the Poisson equation under the spherical coordinate system with Bi-CGSTAB method[J]. Journal of University of Science and Technology of China, 2017, 47(8): 695-698.

用稳定双共轭梯度方法数值求解球坐标系下的Poisson方程

Numerical solution to the Poisson equation under the spherical coordinate system with Bi-CGSTAB method

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