Fast solution of incompressible flow problems with two-level pressure approximation

IF 2.1 2区 数学 Q1 MATHEMATICS, APPLIED
Jennifer Pestana, David J. Silvester
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引用次数: 0

Abstract

This paper develops efficient preconditioned iterative solvers for incompressible flow problems discretised by an enriched Taylor–Hood mixed approximation, in which the usual pressure space is augmented by a piecewise constant pressure to ensure local mass conservation. This enrichment process causes over-specification of the pressure when the pressure space is defined by the union of standard Taylor–Hood basis functions and piecewise constant pressure basis functions, which complicates the design and implementation of efficient solvers for the resulting linear systems. We first describe the impact of this choice of pressure space specification on the matrices involved. Next, we show how to recover effective solvers for Stokes problems, with preconditioners based on the singular pressure mass matrix, and for Oseen systems arising from linearised Navier–Stokes equations, by using a two-stage pressure convection–diffusion strategy. The codes used to generate the numerical results are available online.

Abstract Image

用两级压力近似法快速解决不可压缩流动问题
本文针对通过增强泰勒胡德混合近似离散化的不可压缩流动问题开发了高效的预条件迭代求解器,其中通常的压力空间通过片断恒定压力进行了增强,以确保局部质量守恒。当压力空间由标准泰勒胡德基函数和片断恒定压力基函数联合定义时,这种丰富过程会导致压力的过度指定,从而使设计和实施高效求解器来求解线性系统变得复杂。我们首先描述了压力空间规范的选择对相关矩阵的影响。接下来,我们展示了如何通过使用基于奇异压力质量矩阵的预处理器来恢复斯托克斯问题的有效求解器,以及如何通过使用两阶段压力对流-扩散策略来恢复线性化纳维-斯托克斯方程产生的奥森系统的有效求解器。用于生成数值结果的代码可在线查阅。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Numerische Mathematik
Numerische Mathematik 数学-应用数学
CiteScore
4.10
自引率
4.80%
发文量
72
审稿时长
6-12 weeks
期刊介绍: Numerische Mathematik publishes papers of the very highest quality presenting significantly new and important developments in all areas of Numerical Analysis. "Numerical Analysis" is here understood in its most general sense, as that part of Mathematics that covers: 1. The conception and mathematical analysis of efficient numerical schemes actually used on computers (the "core" of Numerical Analysis) 2. Optimization and Control Theory 3. Mathematical Modeling 4. The mathematical aspects of Scientific Computing
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