Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2004-01, Vol.44 (2), p.135-146
Main Author: Gelfgat, Alexander Yu
Format: Article
Language:English
Subjects:
Hopf bifurcation
natural convection
spectral methods
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Summary:The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time‐dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.624