Stability analysis of the flow in a cubical cavity heated from below

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 1.5×105. 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 equations of motion using a finite-difference solver. Present results show that different stable convective flow patterns can coexist for different ranges of the Rayleigh number.