The stability of two-dimensional (2D) natural convection flows with respect to both two-and
three-dimensional perturbations is investigated numerically. Several methods (Arnoldi's
method, preconditioned Newton's iteration and preconditioned continuation method) are put
together for this purpose and applied to natural convection in a differentially heated square
cavity with conducting horizontal walls for a large range of Prandtl numbers. These methods
are first validated by comparison with results reported in the literature for several Prandtl …