文章基本信息

标题：Resolution and implementation of the nonstationary vorticity velocity pressure formulation of the Navier–Stokes equations
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作者：Mohamed Abdelwahed ; Ebtisam Alharbi ; Nejmeddine Chorfi 等
期刊名称：Boundary Value Problems
印刷版ISSN：1687-2762
电子版ISSN：1687-2770
出版年度：2020
卷号：2020
期号：1
页码：1-19
DOI：10.1186/s13661-020-01464-8
出版社：Hindawi Publishing Corporation
摘要：This paper deals with the iterative algorithm and the implementation of the spectral discretization of time-dependent Navier–Stokes equations in dimensions two and three. We present a variational formulation, which includes three independent unknowns: the vorticity, velocity, and pressure. In dimension two, we establish an optimal error estimate for the three unknowns. The discretization is deduced from the implicit Euler scheme in time and spectral methods in space. We present a matrix linear system and some numerical tests, which are in perfect concordance with the analysis.
关键词：Nonstationary Navier–Stokes equations ; Implicit Euler’s scheme ; Spectral discretization ; GMRES method