TITLE:
Computational bifurcations and stability analysis of the flow in a cubical
cavity heated from below

AUTHORS:
D. Puigjaner^(1), J. Herrero^(2), C. Sim\'o^(3) and F. Giralt$^(2)

(1) Dept. Enginyeria Inform\`atica i Matem\`atiques, ETSE, Univ. Rovira i 
Virgili, Tarragona, Catalunya, Spain

(2) Dept. Enginyeria Qu\'{\i}mica, ETSEQ, Univ. Rovira i Virgili, Tarragona,
Catalunya, Spain.

(3) Dept. Matem\`atica Aplicada i An\`alisi, Univ. de Barcelona, Barcelona,
Catalunya, Spain.

ABSTRACT:
A numerical study of bifurcations and stability of the steady convective
flow of air in a cubical enclosure heated from below was carried out using
a Galerkin spectral method. The set of basis functions was chosen so that 
all boundary conditions and the continuity equation were implicitly satisfied.
A parameter continuation method was applied to determine the steady solutions
and bifurcations of the nonlinear governing equations as a function of Rayleigh
number ($Ra$) for values of $Ra$ up to $1.5\times 10^5$. The eigenvalue problem
associated with the stability analysis of the steady solutions along the
different branches of solutions was solved using the Arnoldi method.
The convergence of the method was consistent with the number of modes used and
the results were also verified by a numerical solution of the unsteady 
equationsof motion using a finite difference solver. Present results show that
different stable convective flow patterns can coexist for different ranges of
the Rayleigh number and clarify incompleteness of previous numerical results
reported in the literature.