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首页> 外文期刊>Mathematical Problems in Engineering >Smoothing Analysis of Distributive Red-Black Jacobi Relaxation for Solving 2D Stokes Flow by Multigrid Method
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Smoothing Analysis of Distributive Red-Black Jacobi Relaxation for Solving 2D Stokes Flow by Multigrid Method

机译：多重网格法求解二维斯托克斯流的红黑雅各布分布松弛的平滑分析

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摘要

Smoothing analysis process of distributive red-black Jacobi relaxation in multigrid method for solving 2D Stokes flow is mainly investigated on the nonstaggered grid by using local Fourier analysis (LFA). For multigrid relaxation, the nonstaggered discretizing scheme of Stokes flow is generally stabilized by adding an artificial pressure term. Therefore, an important problem is how to determine the zone of parameter in adding artificial pressure term in order to make stabilization of the algorithm for multigrid relaxation. To end that, a distributive red-black Jacobi relaxation technique for the 2D Stokes flow is established. According to the 2h-harmonics invariant subspaces in LFA, the Fourier representation of the distributive red-black Jacobi relaxation for discretizing Stokes flow is given by the form of square matrix, whose eigenvalues are meanwhile analytically computed. Based on optimal one-stage relaxation, a mathematical relation of the parameter in artificial pressure term between the optimal relaxation parameter and related smoothing factor is well yielded. The analysis results show that the numerical schemes for solving 2D Stokes flow by multigrid method on the distributive red-black Jacobi relaxation have a specified convergence parameter zone of the added artificial pressure term.
机译：运用局部傅里叶分析（LFA），主要在非交错网格上研究了求解二维斯托克斯流的多网格方法中红黑Jacobi分布松弛的平滑分析过程。对于多网格松弛，通常通过添加人工压力项来稳定Stokes流的非交错离散方案。因此，一个重要的问题是如何在增加人工压力项时确定参数区域，以使多网格松弛算法的稳定性。为此，建立了用于2D Stokes流的分布式红黑Jacobi松弛技术。根据LFA中的2h调和不变子空间，用离散矩阵的形式给出了用于离散Stokes流的分布红黑Jacobi弛豫的傅里叶表示，并对其特征值进行了解析计算。基于最佳的一级松弛，可以很好地得出最佳松弛参数与相关平滑因子之间的人工压力项参数的数学关系。分析结果表明，在分布红黑雅可比弛豫下采用多网格方法求解二维斯托克斯流的数值方案具有增加的人工压力项的指定收敛参数区。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第4期|572198.1-572198.7|共7页
  • 作者

    Zhu Xingwen; Zhang Lixiang;

  • 作者单位

    Dali Univ, Sch Math & Comp, Dali 671003, Yunnan, Peoples R China.;

    Kunming Univ Sci & Technol, Dept Engn Mech, Kunming 650500, Yunnan, Peoples R China.;

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