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Numerical prediction of natural convection in a tall enclosure
Author(s) -
Christopher David M.
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.390
Subject(s) - natural convection , enclosure , galerkin method , flow (mathematics) , mechanics , mathematics , skew , rayleigh number , euler equations , finite element method , convection , mathematical analysis , physics , engineering , thermodynamics , telecommunications , astronomy
Abstract The equations for natural convection flow in a tall cavity were solved for a super‐critical Rayleigh number for which oscillations occur in the flow field and various solutions are possible. The objective was to compare various solution methods for this complex flow situation. The equations were solved using the finite element method with the Galerkin form of the method of weighted residuals with various time integration methods, time steps and grid spacings. The Euler time integration method is unsuitable for this problem because of its excessive dissipation. Fine grid distributions and small time steps were needed to predict accurate values of the average temperatures and velocities in the cavity, with even finer elements and time steps needed to accurately predict the amplitudes of the oscillations. An initially uniform temperature distribution lead to a uniformly oscillating skew‐symmetric flow field. An initially random temperature field lead to a symmetry‐breaking flow field that eventually reached the skew‐symmetric flow field after a long time. Copyright © 2002 John Wiley & Sons, Ltd.