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A finite‐element study of the bénard problem using parameter‐stepping and bifurcation search
Author(s) -
Jackson C. P.,
Winters K. H.
Publication year - 1984
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.1650040203
Subject(s) - jacobian matrix and determinant , finite element method , mathematics , bifurcation , flow (mathematics) , mathematical analysis , geometry , boundary (topology) , mechanics , range (aeronautics) , physics , materials science , nonlinear system , quantum mechanics , thermodynamics , composite material
The problem of fluid motion in a cavity with rigid sidewalls that is heated uniformly from below is studied by the finite‐element method. The techniques of parameter‐stepping and monitoring the determinant of the Jacobian matrix to find bifurcations are used. Results are presented for width‐to‐height ratios in the range 1 to 4, and for three different boundary conditions on the horizontal surfaces, namely both rigid, both free, and rigid bottom with free top. The non‐linear branches above the critical Rayleigh number are examined. Extensions to non‐Boussinesq flow are trivial.