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Stochastic bifurcation analysis of Rayleigh–Bénard convection

Published online by Cambridge University Press:  06 April 2010

DANIELE VENTURI
Affiliation:
Department of Energy, Nuclear and Environmental Engineering, University of Bologna, viale del Risorgimento 2, 40136 Bologna, Italy
XIAOLIANG WAN
Affiliation:
Department of Mathematics, Louisiana State University, 226 Lockett Hall, Baton Rouge, LA 70803-4918, USA
GEORGE EM KARNIADAKIS
Affiliation:
Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA
Corresponding
E-mail address:

Abstract

Stochastic bifurcations and stability of natural convection within two-dimensional square enclosures are investigated by different stochastic modelling approaches. Deterministic stability analysis is carried out first to obtain steady-state solutions and primary bifurcations. It is found that multiple stable steady states coexist, in agreement with recent results, within specific ranges of Rayleigh number. Stochastic simulations are then conducted around bifurcation points and transitional regimes. The influence of random initial flow states on the development of supercritical convection patterns is also investigated. It is found that a multi-element polynomial chaos method captures accurately the onset of convective instability as well as multiple convection patterns corresponding to random initial flow states.

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Copyright © Cambridge University Press 2010

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