算子分裂法求解旋转坐标系下不可压黏性流动

刘海湖 1; 苏剑 2; 高丽敏 3; 李开泰 2; 王尚锦 1

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算子分裂法求解旋转坐标系下不可压黏性流动

专题研究 | 更新时间：2025-12-08

- 算子分裂法求解旋转坐标系下不可压黏性流动
- Operator Splitting Methods for Solution of Incompressible Viscous Flows in a Rotating Frame
- 西安交通大学学报 2007年41卷第7期页码：833-837
- 作者机构：
  
  西安交通大学流体机械及压缩机国家工程研究中心,西安,710049
- 作者简介：
- 基金信息：
  
  : 2006-10-23. 作者简介: 刘海湖(1981～),男,硕士生;王尚锦(联系人),男,教授,博士生导师. 基金项目: 国家自然科学基金资助项目(50306019)
- DOI：
  中图分类号： TP391.7
- 网络首发：2007-07-10，
  
  纸质出版：2007
- 稿件说明：
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刘海湖 1, 苏剑 2, 高丽敏 3, 等. 算子分裂法求解旋转坐标系下不可压黏性流动[J]. 西安交通大学学报, 2007,41(7):833-837.

刘海湖 1, 苏剑 2, 高丽敏 3, et al. Operator Splitting Methods for Solution of Incompressible Viscous Flows in a Rotating Frame[J]. 2007, 41(7): 833-837.
刘海湖 1, 苏剑 2, 高丽敏 3, 等. 算子分裂法求解旋转坐标系下不可压黏性流动[J]. 西安交通大学学报, 2007,41(7):833-837. DOI：

刘海湖 1, 苏剑 2, 高丽敏 3, et al. Operator Splitting Methods for Solution of Incompressible Viscous Flows in a Rotating Frame[J]. 2007, 41(7): 833-837. DOI：

摘要

提出了求解旋转坐标系下的不可压黏性流动问题的θ格式算子分裂算法.通过算子分裂

把不可压缩性、非线性和哥氏力占优三大耦合困难分割开来.采用亚网格尺度稳定化方法消除了Galerkin方法求解时由于不可压缩性和哥氏力占优所引发的数值振荡.结合最小二乘和共轭梯度法间接求解非线性子问题

排除了强对流作用所引发的数值振荡

避免了引入迎风格式离散对流项的必要性.同时该算法保证了迭代过程中有限元总刚度矩阵正定不变的特性

为求解线性方程组采用高效的求解器提供了可能.数值试验表明

该算法具有稳定性好、收敛速度快、计算精度高的特点.

Abstract

An operator splitting method was developed to solve the incompressible Navier-Stokes equations defined in a rotating frame of reference. Based on the operator splitting

this method provides an efficient way to decouple the three main difficulties of the problem

the incompressibility

the nonlinearity and the numerical oscillations due to the presence of the dominated Coriolis forces. The sub-grid scale stabilized method was used to eliminate the oscillations caused by incompressibility and dominated Coriolis forces when Galerkin method was employed. Least-squares conjugate gradient algorithms were applied to solve for the nonlinear instability

which avoids the necessity of introducing the upwind scheme to discrete the convective term. Compared with other numerical methods

the present method ensures the resulting coefficient matrices to be positive definite and invariable

which can be efficiently stored and solved. Several numerical examples indicate that the method displays improved stability

fast convergence and high accuracy.

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Keywords

references

Codina R,Soto O. Finite element solution of the Stokes problem with dominating Coriolis force[J]. Computer Methods in Applied Mechanics and Engineering,1997,142:215-234.

Codina R. Numerical solution of the incompressible Navier-Stokes equations with Coriolis forces based on the discretization of the total time derivative[J]. Journal of Computational Physics,1999,148:467-496.

Codina R. A stabilized finite element method for generalized stationary incompressible flows[J]. Computer Methods in Applied Mechanics and Engineering,2001,190:2681-2706.

刘海湖,李开泰,苏剑,等. 采用算子分裂法求解不可压黏性流动[J]. 西安交通大学学报,2006,40(12):1270-1272.

Liu Haihu, Li Kaitai,Su Jian, et al. Operator splitting methods for solution of incompressible viscous flows[J]. Journal of Xi'an Jiaotong University,2006,40(12):1270-1272.

Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation[J]. Computer Methods in Applied Mechanics and Engineering,1998,156:185-210.

Glowinski R. Finite element methods for incompressible viscous flow[M].Amsterdam,Netherlands:North-Holland, 2003.

Haroon S K,Scriven L E. Viscous flow through a rotating square channel[J]. Physics of Fluids,1985,28(10):2968-2979.

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