A practical review on linear and nonlinear global approaches to flow instabilities
APPLIED MECHANICS REVIEWS(2019)
摘要
This paper aims at reviewing linear and nonlinear approaches to study the stability of fluid flows. We provide a concise but self-contained exposition of the main concepts and specific numerical methods designed for global stability studies, including the classical linear stability analysis, the adjoint-based sensitivity, and the most recent nonlinear developments. Regarding numerical implementation, a number of ideas making resolution particularly efficient are discussed, including mesh adaptation, simple shift-invert strategy instead of the classical Arnoldi algorithm, and a simplification of the recent nonlinear self-consistent (SC) approach proposed by Mantic-Lugo et al. (2014, "Self-Consistent Mean Flow Description of the Nonlinear Saturation of the Vortex Shedding in the Cylinder Wake," Phys. Rev. Lett., 113(8), p. 084501). An open-source software implementing all the concepts discussed in this paper is provided. The software is demonstrated for the reference case of the two-dimensional (2D) flow around a circular cylinder, in both incompressible and compressible cases, but is easily customizable to a variety of other flow configurations or flow equations.
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