An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
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DOI：
10.1006/jcph.1997.5651
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发表时间：
1997-05-01
影响因子：
4.1
通讯作者：
Fischer, PF
中科院分区：
文献类型：
--
作者：
Fischer, PF
复杂区域中Navier-Stokes方程的有效解依赖于稀疏线性系统的快速求解器的可用性。对于非定常不可压缩流，压力算子是刚度的主要贡献者，因为特征传播速度是无穷大的。在算子分裂公式的上下文中，压力求解是计算上最具挑战性的，尽管其起源是椭圆的。我们研究了不可压缩Navier-Stokes方程的P-N - PN-2谱元公式中的一致L-2 Poisson算子的几个预条件子。我们开发了一个基于有限元的添加剂施瓦茨预处理器使用重叠子域加上一个粗网格投影算子，直接施加到内部高斯点的压力。对于大的二维问题，这种方法可以产生多达五倍的减少模拟时间比以前采用的方法的基础上放气。(C)北京：科学出版社.
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We examine several preconditioners for the consistent L-2 Poisson operator arising in the P-N - PN-2 spectral element formulation of the incompressible Navier-Stokes equations. We develop a finite element-based additive Schwarz preconditioner using overlapping subdomains plus a coarse grid projection operator which is applied directly to the pressure on the interior Gauss points. For large two-dimensional problems this approach can yield as much as a fivefold reduction in simulation time over previously employed methods based upon deflation. (C) 1997 Academic Press.