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A practical review on linear and nonlinear global approaches to flow instabilities

Fabre, David and Citro, Vincenzo and Sabino, Diogo and Bonnefis, Paul and Sierra Ausin, Javier and Giannetti, Flavio and Pigou, Maxime A practical review on linear and nonlinear global approaches to flow instabilities. (2018) Applied Mechanics Reviews, 70 (6). 060802. ISSN 0003-6900

(Document in English)

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Official URL: https://doi.org/10.1115/1.4042737


This paper aims at reviewing linear and nonlinear approaches to study the stability offluid flows. We provide a concise but self-contained exposition of the main concepts andspecific numerical methods designed for global stability studies, including the classicallinear stability analysis, the adjoint-based sensitivity, and the most recent nonlineardevelopments. Regarding numerical implementation, a number of ideas making resolu-tion particularly efficient are discussed, including mesh adaptation, simple shift-invertstrategy instead of the classical Arnoldi algorithm, and a simplification of the recent non-linear self-consistent (SC) approach proposed by Manticˇ-Lugo et al. (2014, “Self-Consistent Mean Flow Description of the Nonlinear Saturation of the Vortex Shedding inthe Cylinder Wake,” Phys. Rev. Lett., 113(8), p. 084501). An open-source software imple-menting all the concepts discussed in this paper is provided. The software is demon-strated for the reference case of the two-dimensional (2D) flow around a circularcylinder, in both incompressible and compressible cases, but is easily customizable to avariety of other flow configurations or flow equations.

Item Type:Article
HAL Id:hal-03240798
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Università degli Studi di Salerno - UniSa (ITALY)
Laboratory name:
Deposited On:18 May 2021 15:02

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