Numerical study on the transition of natural convection in a cubic box

A difference method of spatially fourth order accuracy on the staggerd mesh points is applied to study the transition of natural convection in a cubic box heated from below with insulating sidewalls. Special attentions are paid to the sensitivity of the solution on the degree of spatial resolution and transformation way of the coordinate variables to concentrate mesh points near the boundaries. As a preliminary study, numerical solutions of the cavity flow are computed. The present results agree with those obtained by the methods with high accuracy reported in the previous paper. It is found that the natural convection which initially grows symmetrically with respect to the vertical center line, changes to a lateral single roll as time proceeds. The critical Rayleigh number is about 6 050 slightly smaller than 6 798 which has been obtained for the fixed boundary condition by use of the linear stability analysis (Mizushima et al. 1997).