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

David Fabre (1) , Vincenzo Citro (2) , Diogo Sabino (1) , Paul Bonnefis (1) , Javier Sierra Ausin (1) , Flavio Giannetti (2) , Maxime Pigou (1)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 UNISA - Università degli Studi di Salerno = University of Salerno

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.

Mots clés: Instabilities

Domaines: Mécanique des fluides [physics.class-ph]

David Fabre, Vincenzo Citro, Diogo Sabino, Paul Bonnefis, Javier Sierra Ausin, et al.. A practical review on linear and nonlinear global approaches to flow instabilities. Applied Mechanics Reviews, 2018, 70 (6), pp.060802. ⟨10.1115/1.4042737⟩. ⟨hal-03240798⟩