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Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (2): 237-258.doi: https://doi.org/10.1007/s10483-014-1787-6

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New nonconforming finite element method for solving transient Naiver-Stokes equations

谢春梅1 冯民富2   

  1. 1. School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China;
    2. School of Mathematics, Sichuan University, Chengdu 610064, P. R. China
  • 收稿日期:2012-11-22 修回日期:2013-06-14 出版日期:2014-02-27 发布日期:2014-02-18

New nonconforming finite element method for solving transient Naiver-Stokes equations

 XIE Chun-Mei1, FENG Min-Fu2   

  1. 1. School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China;
    2. School of Mathematics, Sichuan University, Chengdu 610064, P. R. China
  • Received:2012-11-22 Revised:2013-06-14 Online:2014-02-27 Published:2014-02-18

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343

被引次数

2

摘要： For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., PNC1 /PNC1 triangular and PNQ1 /PNQ1 quadrilateral finite element spaces. The semiand full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features: avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.

关键词: transient Naiver-Stokes problem, nonconforming finite element method, pressure projection, variational multiscale method, 功能梯度材料, 半解析法, 复杂形状, 开孔, 三维分析

Abstract: For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., PNC1 /PNC1 triangular and PNQ1 /PNQ1 quadrilateral finite element spaces. The semiand full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features: avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.

Key words: transient Naiver-Stokes problem, nonconforming finite element method, pressure projection, variational multiscale method, functionally graded material, semi-analytical
method, complex shape, 3D analysis, hole

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