计算物理 ›› 2017, Vol. 34 ›› Issue (6): 657-665.DOI: 10.19596/j.cnki.1001-246x.7569

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大雷诺数Navier-Stokes方程的两水平亚格子模型稳定化方法

杨晓成, 尚月强   

  1. 西南大学 数学与统计学院, 重庆 400715
  • 收稿日期:2016-11-01 修回日期:2017-03-27 出版日期:2017-11-25 发布日期:2017-11-25
  • 通讯作者: 尚月强(1976-),男,教授,从事偏微分方程数值解研究,E-mail:yqshang@swu.edu.cn
  • 作者简介:杨晓成(1989-),男,硕士生,从事偏微分方程数值解研究,E-mail:yxc1214@email.swu.edu.cn
  • 基金资助:
    国家自然科学基金(11361016)及重庆市基础与前沿研究计划(cts2016jcyjA0348)资助项目

Two-level Subgrid Stabilized Methods for Navier-Stokes Equations at High Reynolds Numbers

YANG Xiaocheng, SHANG Yueqiang   

  1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
  • Received:2016-11-01 Revised:2017-03-27 Online:2017-11-25 Published:2017-11-25

摘要: 基于两重网格离散方法,提出三种求解大雷诺数定常Navier-Stokes方程的两水平亚格子模型稳定化有限元算法.其基本思想是首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程,然后在细网格上分别用三种不同的校正格式求解一个亚格子模型稳定化的线性问题,以校正粗网格解.通过适当的稳定化参数和粗细网格尺寸的选取,这些算法能取得最优渐近收敛阶的有限元解.最后,用数值模拟验证三种算法的有效性.

关键词: Navier-Stokes方程, 亚格子模型, 有限元方法, 大雷诺数流

Abstract: Based on two-grid discretizations,three two-level subgrid stabilized finite element algorithms for stationary Navier-Stokes equations at high Reynolds numbers are proposed and compared. Basic idea of the algorithms is to solve a fully nonlinear Navier-Stokes problem with a subgrid stabilization term on a coarse grid,and then solve a subgrid stabilized linear fine grid problem based on one step of Newton,Oseen or Stokes iterations for Navier-Stokes equations.It shows that with suitable stabilization parameters and coarse and fine grid sizes,those algorithms yield an optimal convergence rate. Finally, numerial results are given to show efficiency of the algorithms.

Key words: Navier-Stokes equations, subgrid model, finite element method, high Reynolds number flow

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