Oscillatory instability of natural convection of air in a laterally heated cube: DNS vs linear stability analysis

Nowadays, when three-dimensional computations replace two-dimensional ones, we make an attempt to extend a classical benchmark on two-dimensional convection of air in a laterally heated square box [1] to a three-dimensional formulation. We focus not only on the steady state flows, but also on the transition to unsteadiness (oscillatory instability), as it was done for the two-dimensional problem in, e.g., in [2] and references therein. It is well known that correct computation of a bifurcation point requires an accurate numerical representation of both steady flow state and the most unstable perturbation (eigenvector of the linearized stability problem), which makes it a noticeably more challanging problem.