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首页> 外文期刊>Mathematical Problems in Engineering >A New Reduced Stabilized Mixed Finite-Element Method Based on Proper Orthogonal Decomposition for the Transient Navier-Stokes Equations
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A New Reduced Stabilized Mixed Finite-Element Method Based on Proper Orthogonal Decomposition for the Transient Navier-Stokes Equations

机译：瞬态Navier-Stokes方程的基于正交分解的新型简化稳定混合有限元方法

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摘要

A reduced stabilized mixed finite-element (RSMFE) formulation based on proper orthogonal decomposition (POD) for the transient Navier-Stokes equations is presented. An ensemble of snapshots is compiled from the transient solutions derived from a stabilized mixed finite-element (SMFE) method based on two local Gauss integrations for the two-dimensional transient Navier-Stokes equations by using the lowest equal-order pair of finite elements. Then, the optimal orthogonal bases are reconstructed by implementing POD techniques for the ensemble snapshots. Combining POD with the SMFE formulation, a new low-dimensional and highly accurate SMFE method for the transient Navier-Stokes equations is obtained. The RSMFE formulation could not only greatly reduce its degrees of freedom but also circumvent the constraint of inf-sup stability condition. Error estimates between the SMFE solutions and the RSMFE solutions are derived. Numerical tests confirm that the errors between the RSMFE solutions and the SMFE solutions are consistent with the the theoretical results. Conclusion can be drawn that RSMFE method is feasible and efficient for solving the transient Navier-Stokes equations.
机译：针对瞬态Navier-Stokes方程，提出了一种基于适当正交分解（POD）的简化稳定混合有限元（RSMFE）公式。通过使用最低等阶有限元对，基于二维局部暂态Navier-Stokes方程的两个局部高斯积分，从稳定混合有限元（SMFE）方法得到的暂态解中编译出快照集合。然后，通过对整体快照实施POD技术来重建最佳正交基。结合POD和SMFE公式，获得了用于瞬态Navier-Stokes方程的新的低维，高精度SMFE方法。 RSMFE公式不仅可以大大降低其自由度，而且还可以规避INF稳定条件的约束。得出SMFE解决方案和RSMFE解决方案之间的误差估计。数值试验证明，RSMFE解和SMFE解之间的误差与理论结果一致。可以得出结论，RSMFE方法对于求解瞬态Navier-Stokes方程是可行且有效的。

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  • 来源
    《Mathematical Problems in Engineering》 |2011年第2期|p.1-19|共19页
  • 作者

    Aiwen Wang; Jian Li; Zhenhua Di; Xiangjun Tian; Dongxiu Xie;

  • 作者单位

    School of Applied Science, Beijing Information Science and Technobgy University, Beijing 100192, China;

    Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721007, China;

    College of Global Change and Earth System Science, Beijing Normal University, Beijing 100009, China;

    Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;

    School of Applied Science, Beijing Information Science and Technobgy University, Beijing 100192, China;

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