A Domain Decomposition Matrix - Free Method for Global Linear Stability

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThis work is dedicated to present a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains.An Arnoldi technique based on snapshots in subdomains of the entire geometry combined with a multidomains linearized DNS based on an influence matrix with respect to finite difference schemes is adopted and illustrated on three benchmark problems: the lid-driven cavity, the square cylinder and the open cavity flow.The efficiency of the method to extract large scale structures in a multidomains framework is emphasized. Such a method appears thus a promising tool to deal with large computational domains and three-dimensionality within a parallel architecture. NotationsIn this section, the notations used for domains decomposition method are given below:• D is the computational domain.• ∂D is the boundary of D.• N b denotes the number of subdomains which composes D• ∂D i denotes the boundary of D i .• Υ i is the union of all the interfaces of the subdomain D i .• N i : number of nodes of the interface Υ i .• {γ i,j } k=1,N i references the nodes of Υ i .• χ i represents the boundary except the interface of the subdomain D i :

Centrifugal instabilities in an experimental open cavity flow

“…Cavity flows belong to the family of impinging shear layers and meet the expectations of fundamental and applied research. However, it has been recently shown that the first instability does not occur in the shear layer but inside the cavity, as shown in Brès & Colonius (2008), Meseguer-Garrido et al (2011), Alizard, Robinet & Gloerfelt (2012). As reported in these studies, frequencies associated with the inner-flow structures are approximately two orders of magnitude smaller than the dominant (shear-layer) frequencies (see also Basley et al 2013Basley et al , 2014).…”

Flow control design inspired by linear stability analysis

“…A new time-stepping shift-invert algorithm based on a Krylov subspace iteration for linear stability analysis of large-scale problems is proposed in [19] having the advantage of converging to specific parts of the global spectrum. In [7] a matrix-free method is proposed for global stability analysis based on a multi-domain DNS code, discretizing the equations in multi-connected rectangular subdomains and using an Arnoldi method. In [101] matrix-free method is proposed for the computation of the perturbation fields induced by harmonic forcing of the linearised Navier-Stokes equations.…”

“…This value of the critical Reynolds number is in excellent agreement with works of other authors. 5,7,11 Other 2D examples considered in the following are the flow in an open cavity with an incoming thin and controlled boundary layer and the flow in a suddenly expanded channel, whose stability spectra are shown in Fig. 2(a) and (b), respectively.…”

Instability Analysis of Incompressible Open Cavity Flows

“…Basley et al [15] used time-resolved particle image velocimetry (PIV) to extract the spatial distribution of the most characteristic frequencies in the incompressible open cavity with two different aspect ratios, and also identified once again the presence of the aforementioned shear layer modes in the incompressible regime. Alizard et al [6] focused on the global instability analysis of open flows using a domain decomposition matrix-free method. One of the benchmark problems the latter authors employed is the square cavity, where, at a single Reynolds number, the three-dimensional spanwise periodic leading perturbations were identified.…”

“…Perturbations that are of the size of the cavity depth, β 6, Critical values are cited in table 4. 6.…”