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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (9): 1083-1096.doi: https://doi.org/10.1007/s10483-013-1729-x

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Finite difference streamline diffusion method using nonconforming space for incompressible time-dependent Navier-Stokes equations

陈刚1 冯民富1 何银年2   

  1. 1. Department of Mathematics, Sichuan University, Chengdu 610064, P.R. China;
    2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P.R. China
  • 收稿日期:2012-05-09 修回日期:2013-03-01 出版日期:2013-09-02 发布日期:2013-09-02

Finite difference streamline diffusion method using nonconforming space for incompressible time-dependent Navier-Stokes equations

CHEN Gang1, FENG Min-Fu1, HE Yin-Nian2   

  1. 1. Department of Mathematics, Sichuan University, Chengdu 610064, P.R. China;
    2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P.R. China
  • Received:2012-05-09 Revised:2013-03-01 Online:2013-09-02 Published:2013-09-02

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摘要： This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart (CR) element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.

关键词: Navier-Stokes equation, high Reynolds number, Ladyzhenskaya-Babuˇska-Brezzi (LBB) condition, finite difference streamline diffusion method, discrete Gronwall’s inequality

Abstract: This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart (CR) element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.

Key words: inverse problems, nonlinear ill-posed operator equations, Newton type method, implicit iterative method, iteration stopping rule, Navier-Stokes equation, high Reynolds number, Ladyzhenskaya-Babuˇska-Brezzi (LBB) condition, finite difference streamline diffusion method, discrete Gronwall’s inequality

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