Natural convection in a cubic cavity: Implicit numerical solution of two benchmark problems

Natural convection of air within a cubic cavity, two opposite walls of which are differentially heated, is simulated numerically for Rayleigh numbers of 10(3) , 10(4) , 10(5) , and 10(6) . For each Rayleigh number, two benchmark problems are examined: all four remaining walls are either adiabatic or perfectly conducting. The conservation equations, written using a vorticity-velocity formulation, are discretized with second-order finite differences on uniform grids containing up to 81(3) points. The equations are solved at all points simultaneously using Newton's method. Solutions on an 81(3) nonuniform grid are also presented. Excellent agreement with published computational and experimental data is observed, and new benchmark data are reported for the second problem.