Ay. Gelfgat, Different modes of Rayleigh-Benard instability in two- and three-dimensional rectangular enclosures, J COMPUT PH, 156(2), 1999, pp. 300-324
The article describes a complete numerical solution of a recently formulate
d benchmark problem devoted to the parametric study of Rayleigh-Benard inst
ability in rectangular two- and three-dimensional boxes. The solution is ca
rried out by the spectral Galerkin method with globally defined, three-dime
nsional, divergent-free basis functions, which satisfy all boundary conditi
ons. The general description of these three-dimensional basis functions, wh
ich can be used for a rather wide spectrum of problems, is presented. The r
esults of the parametric calculations are presented as neutral curves showi
ng the dependence of the critical Rayleigh number on the aspect ratio of th
e cavity. The neutral curves consist of several continuous branches, which
belong to different modes of the most dangerous perturbation. The patterns
of different perturbations are also reported. The results obtained lead Co
some new conclusions about the patterns of the most dangerous perturbations
and about the similarities between two- and three-dimensional models. Same
extensions of the considered benchmark problem are discussed. (C) 1999 Aca
demic Press.