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Numerical investigation of the first instabilities in the differentially heated 8:1 cavity
Author(s) -
Auteri F.,
Parolini N.
Publication year - 2002
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.398
Subject(s) - galerkin method , hopf bifurcation , flow (mathematics) , mechanics , natural convection , symmetry (geometry) , projection (relational algebra) , bifurcation , rayleigh number , periodic boundary conditions , physics , symmetry breaking , legendre polynomials , mathematics , rayleigh scattering , convection , classical mechanics , boundary value problem , mathematical analysis , geometry , thermodynamics , optics , nonlinear system , finite element method , algorithm , quantum mechanics
We present a new Galerkin–Legendre spectral projection solver for the simulation of natural convection in a differentially heated cavity. The projection method is applied to the study of the first non‐stationary instabilities of the flow in a 8:1 cavity. Statistics of the periodic solution are reported for a Rayleigh number of 3.4×10 5 . Moreover, we investigate the location and properties of the first Hopf bifurcation and of the three successive bifurcations. The results confirm the previous finding in the range of Rayleigh numbers investigated that the flow instabilities originate in the boundary layer on the vertical walls. A peculiar phenomenon of symmetry breaking and symmetry restoring is observed portraying the first steps of the transition to chaos for this flow. Copyright © 2002 John Wiley & Sons, Ltd.