On the convergence of the Rhie–Chow stabilized Box method for the Stokes problem

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
G. Negrini, N. Parolini, M. Verani
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引用次数: 0

Abstract

The finite volume method (FVM) is widely adopted in many different applications because of its built-in conservation properties, its ability to deal with arbitrary mesh and its computational efficiency. In this work, we consider the Rhie–Chow stabilized Box method (RCBM) for the approximation of the Stokes problem. The Box method (BM) is a piecewise linear Petrov–Galerkin formulation on the Voronoi dual mesh of a Delaunay triangulation, whereas the Rhie–Chow (RC) stabilization is a well known stabilization technique for FVM. The first part of the article provides a variational formulation of the RC stabilization and discusses the validity of crucial properties relevant for the well-posedness and convergence of RCBM. Moreover, a numerical exploration of the convergence properties of the method on 2D and 3D test cases is presented. The last part of the article considers the theoretically justification of the well-posedness of RCBM and the experimentally observed convergence rates. This latter justification hinges upon suitable assumptions, whose validity is numerically explored.

论斯托克斯问题的瑞-周稳定盒方法的收敛性
有限体积法(FVM)因其内在的守恒特性、处理任意网格的能力和计算效率,在许多不同的应用中被广泛采用。在这项工作中,我们考虑用 Rhie-Chow 稳定盒方法(RCBM)来逼近斯托克斯问题。方框法(BM)是一种在 Delaunay 三角剖分的 Voronoi 对偶网格上的片断线性 Petrov-Galerkin 公式,而 Rhie-Chow (RC) 稳定是一种众所周知的 FVM 稳定技术。文章的第一部分提供了 RC 稳定的变分公式,并讨论了与 RCBM 的好求和收敛性相关的关键属性的有效性。此外,文章还对该方法在二维和三维测试案例中的收敛特性进行了数值探索。文章的最后一部分从理论上论证了 RCBM 的假设性和实验观察到的收敛率。后一部分的论证取决于适当的假设,并对其有效性进行了数值探讨。
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
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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