数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 1981-2000.doi: 10.1007/s10473-022-0515-z

• 论文 • 上一篇    

NUMERICAL ANALYSIS OF A BDF2 MODULAR GRAD-DIV STABILITY METHOD FOR THE STOKES/DARCY EQUATIONS

Jiangshan WANG1, Lingxiong MENG1, Xiaofeng JIA2, Hongen JIA3   

  1. 1. College of Mathematics, Taiyuan University of Technology, Tai'yuan, 030024, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China;
    3. College of Mathematics, Taiyuan University of Technology, Tai'yuan, 030024, China
  • 收稿日期:2020-09-06 修回日期:2022-05-31 发布日期:2022-11-02
  • 通讯作者: Hongen Jia,E-mail:jiahongen@aliyun.com E-mail:jiahongen@aliyun.com
  • 基金资助:
    Supported by the Provincial Natural Science Foundation of Shanxi (201901D111123), Key Research and Development (R&D) Projects of Shanxi Province (201903D121038).

NUMERICAL ANALYSIS OF A BDF2 MODULAR GRAD-DIV STABILITY METHOD FOR THE STOKES/DARCY EQUATIONS

Jiangshan WANG1, Lingxiong MENG1, Xiaofeng JIA2, Hongen JIA3   

  1. 1. College of Mathematics, Taiyuan University of Technology, Tai'yuan, 030024, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China;
    3. College of Mathematics, Taiyuan University of Technology, Tai'yuan, 030024, China
  • Received:2020-09-06 Revised:2022-05-31 Published:2022-11-02
  • Contact: Hongen Jia,E-mail:jiahongen@aliyun.com E-mail:jiahongen@aliyun.com
  • Supported by:
    Supported by the Provincial Natural Science Foundation of Shanxi (201901D111123), Key Research and Development (R&D) Projects of Shanxi Province (201903D121038).

摘要: In this paper, a BDF2 modular grad-div algorithm for the Stokes/Darcy model is constructed. This method not only effectively avoids solver breakdown, but also increases computational efficiency for increasing parameter values. Herein, complete stability and error analysis are provided. Finally, some numerical tests are proposed to justify the theoretical analysis.

关键词: Stokes/Darcy model, decoupling method, BDF2 modular grad-div

Abstract: In this paper, a BDF2 modular grad-div algorithm for the Stokes/Darcy model is constructed. This method not only effectively avoids solver breakdown, but also increases computational efficiency for increasing parameter values. Herein, complete stability and error analysis are provided. Finally, some numerical tests are proposed to justify the theoretical analysis.

Key words: Stokes/Darcy model, decoupling method, BDF2 modular grad-div

中图分类号: 

  • 58F15