A general methodology for investigating flow instabilities in complex geometries: application to natural convection in enclosures

This paper presents a general methodology for studying instabilities of nat ural convection flows enclosed in cavities of complex geometry. Different t ools have been developed, consisting of time integration of the unsteady eq uations, steady state solving, and computation of the most unstable eigenmo des of the Jacobian and its adjoint. The methodology is validated in the cl assical differentially heated cavity, where the steady solution branch is f ollowed for vary large values of the Rayleigh number and most unstable eige nmodes are computed at selected Rayleigh values. Its effectiveness for comp lex geometries is illustrated on a configuration consisting of a cavity wit h internal heated partitions. We finally propose to reduce the Navier-Stoke s equations to a differential system by expanding the unsteady solution as the sum of the steady state solution and of a linear combination of the lea ding eigenmodes. The principle of the method is exposed and preliminary res ults are presented. Copyright (C) 2001 John Wiley & Sons, Ltd.