Instability of natural convection in a laterally heated cube with perfectly conducting horizontal boundaries

Oscillatory instability of buoyancy convection in a laterally heated cube with perfectly thermally conducting horizontal boundaries is studied. The effect of the spanwise boundaries on the oscillatory instability onset is examined. The problem is treated by Krylov-subspace-iteration-based Newton and Arnoldi methods. The Krylov basis vectors are calculated by a novel approach that involves the SIMPLE iteration and a projection onto a space of functions satisfying all linearized and homogeneous boundary conditions. The finite volume grid is gradually refined from 100 ³ to 256 ³ finite volumes. A self-sustaining oscillatory process responsible for the instability onset is revealed, visualized and explained.