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Direct Simulation of Low‐Re Flow around a Square Cylinder by Numerical Manifold Method for Navier‐Stokes Equations

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  • Zhengrong Zhang
  • Xiangwei Zhang

Abstract

Numerical manifold method was applied to directly solve Navier‐Stokes (N‐S) equations for incompressible viscous flow in this paper, and numerical manifold schemes for N‐S equations coupled velocity and pressure were derived based on Galerkin weighted residuals method as well. Mixed cover with linear polynomial function for velocity and constant function for pressure was employed in finite element cover system. As an application, mixed cover 4‐node rectangular manifold element has been used to simulate the incompressible viscous flow around a square cylinder in a channel. Numerical tests illustrate that NMM is an effective and high‐order accurate numerical method for incompressible viscous flow N‐S equations.

Suggested Citation

  • Zhengrong Zhang & Xiangwei Zhang, 2012. "Direct Simulation of Low‐Re Flow around a Square Cylinder by Numerical Manifold Method for Navier‐Stokes Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:465972
    DOI: 10.1155/2012/465972
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    References listed on IDEAS

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    1. Petra Pořízková & Karel Kozel & Jaromír Horáček, 2012. "Numerical Simulation of Unsteady Compressible Flow in Convergent Channel: Pressure Spectral Analysis," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, May.
    2. Liyun Zhang & Zhangxin Chen, 2011. "A Stabilized Mixed Finite Element Method for Single-Phase Compressible Flow," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-16, January.
    3. Liyun Zhang & Zhangxin Chen, 2011. "A Stabilized Mixed Finite Element Method for Single‐Phase Compressible Flow," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    4. Petra Pořízková & Karel Kozel & Jaromír Horáček, 2012. "Numerical Simulation of Unsteady Compressible Flow in Convergent Channel: Pressure Spectral Analysis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. M. Goodarzi & M. R. Safaei & A. Karimipour & K. Hooman & M. Dahari & S. N. Kazi & E. Sadeghinezhad, 2014. "Comparison of the Finite Volume and Lattice Boltzmann Methods for Solving Natural Convection Heat Transfer Problems inside Cavities and Enclosures," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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