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Open AccessArticle

Numerical Solution of the Navier–Stokes Equations Using Multigrid Methods with HSS-Based and STS-Based Smoothers

by Galina Muratova 1,*,†,‡, Tatiana Martynova 1,†,‡, Evgeniya Andreeva 1,†, Vadim Bavin 1,† and Zeng-Qi Wang 2
1
Mechanics and Computer Science, Vorovich Institute of Mathematics, Southern Federal University, Rostov-on-Don 344000, Russia
2
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200000, China
*
Author to whom correspondence should be addressed.
Current address: 200/1 Stachki Ave., Bld. 2, Rostov-on-Don 344090, Russia.
These authors contributed equally to this work.
Symmetry 2020, 12(2), 233; https://doi.org/10.3390/sym12020233
Received: 29 November 2019 / Revised: 16 January 2020 / Accepted: 21 January 2020 / Published: 4 February 2020
(This article belongs to the Special Issue Mesh Methods - Numerical Analysis and Experiments)
Multigrid methods (MGMs) are used for discretized systems of partial differential equations (PDEs) which arise from finite difference approximation of the incompressible Navier–Stokes equations. After discretization and linearization of the equations, systems of linear algebraic equations (SLAEs) with a strongly non-Hermitian matrix appear. Hermitian/skew-Hermitian splitting (HSS) and skew-Hermitian triangular splitting (STS) methods are considered as smoothers in the MGM for solving the SLAE. Numerical results for an algebraic multigrid (AMG) method with HSS-based smoothers are presented. View Full-Text
Keywords: multigrid methods; Hermitian/skew-Hermitian splitting method; skew-Hermitian triangular splitting method; strongly non-Hermitian matrix multigrid methods; Hermitian/skew-Hermitian splitting method; skew-Hermitian triangular splitting method; strongly non-Hermitian matrix
MDPI and ACS Style

Muratova, G.; Martynova, T.; Andreeva, E.; Bavin, V.; Wang, Z.-Q. Numerical Solution of the Navier–Stokes Equations Using Multigrid Methods with HSS-Based and STS-Based Smoothers. Symmetry 2020, 12, 233.

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