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首页> 外文期刊>International Journal for Numerical Methods in Fluids >Analysis of preconditioned iterative solvers for incompressible flow problems
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Analysis of preconditioned iterative solvers for incompressible flow problems

机译：不可迭代流问题的预处理迭代求解器分析

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摘要

Solving efficiently the incompressible Navier-Stokes equations is a major challenge, especially in the three-dimensional case. The approach investigated by Elman et al. (Finite Elements and Fast Iterative Solvers. Oxford University Press: Oxford, 2005) consists in applying a preconditioned GMRES method to the linearized problem at each iteration of a nonlinear scheme. The preconditioner is built as an approximation of an ideal block-preconditioner that guarantees convergence in 2 or 3 iterations. In this paper, we investigate the numerical behavior for the three-dimensional lid-driven cavity problem with wedge elements; the ultimate motivation of this analysis is indeed the development of a preconditioned Krylov solver for stratified oceanic flows which can be efficiently tackled using such meshes. Numerical results for steady-state solutions of both the Stokes and the Navier-Stokes problems are presented. Theoretical bounds on the spectrum and the rate of convergence appear to be in agreement with the numerical experiments. Sensitivity analysis on different aspects of the structure of the preconditioner and the block decomposition strategies are also discussed.
机译：有效地解决不可压缩的Navier-Stokes方程是一项重大挑战，尤其是在三维情况下。 Elman等人研究的方法。 （有限元和快速迭代求解器。牛津大学出版社：牛津，2005年）在于在非线性方案的每次迭代中将预处理的GMRES方法应用于线性化问题。前置调节器是作为理想的块前置调节器的近似值而构建的，它保证了2或3次迭代的收敛性。在本文中，我们研究了带有楔形单元的三维盖子驱动空腔问题的数值行为。该分析的最终动机确实是针对分层海洋流开发了预处理的Krylov解算器，可以使用此类网格有效地对其进行处理。给出了Stokes和Navier-Stokes问题的稳态解的数值结果。频谱和收敛速度的理论界限似乎与数值实验一致。还讨论了预处理器结构不同方面的敏感性分析和块分解策略。

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