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Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method
Author(s) -
Gelfgat Alexander Yu.
Publication year - 2003
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.624
Subject(s) - galerkin method , natural convection , oscillation (cell signaling) , mathematics , boussinesq approximation (buoyancy) , mechanics , supercritical fluid , benchmark (surveying) , convection , rayleigh number , flow (mathematics) , mathematical analysis , physics , classical mechanics , thermodynamics , geology , chemistry , finite element method , geodesy , biochemistry
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.