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A new full discrete stabilized viscosity method for transient Navier-Stokes equations

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Abstract

A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number (small viscosity coefficient) is proposed based on the pressure projection and the extrapolated trapezoidal rule. The transient Navier-Stokes equations are fully discretized by the continuous equal-order finite elements in space and the reduced Crank-Nicolson scheme in time. The new stabilized method is stable and has many attractive properties. First, the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pressure projection term. Second, the artifical viscosity parameter is added to the viscosity coefficient as a stability factor, so the system is antidiffusive. Finally, the method requires only the solution to a linear system at every time step. Stability and convergence of the method is proved. The error estimation results show that the method has a second-order accuracy, and the constant in the estimation is independent of the viscosity coefficient. The numerical results are given, which demonstrate the advantages of the method presented.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641112, Sichuan Province, P. R. China

    Yan-mei Qin  (覃燕梅)

  2. Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang, 641112, Sichuan Province, P. R. China

    Yan-mei Qin  (覃燕梅)

  3. School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China

    Min-fu Feng  (冯民富)

  4. School of Mathematics, Sichuan University, Chengdu, 610054, P. R. China

    Min-fu Feng  (冯民富)

  5. Institute of Aeronautical Computing Techniques, Xi’an, 710078, P. R. China

    Tian-xiao Zhou  (周天孝)

Authors
  1. Yan-mei Qin  (覃燕梅)
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  2. Min-fu Feng  (冯民富)
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  3. Tian-xiao Zhou  (周天孝)
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Corresponding author

Correspondence to Min-fu Feng  (冯民富).

Additional information

Communicated by Zhe-wei ZHOU

Project supported by the Sichuan Science and Technology Project (No. 05GG006-006-2) and the Research Fund for Introducing Intelligence of Electronic Science and Technology of China

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Qin, Ym., Feng, Mf. & Zhou, Tx. A new full discrete stabilized viscosity method for transient Navier-Stokes equations. Appl. Math. Mech.-Engl. Ed. 30, 839–852 (2009). https://doi.org/10.1007/s10483-009-0704-z

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  • DOI: https://doi.org/10.1007/s10483-009-0704-z

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2000 Mathematics Subject Classification

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