Simulation of natural convection in a vertical enclosure by using a new incompressible flow formulation—pseudovorticity-velocity formulation

Numerical simulations incorporating a new incompressible viscous flow formulation, the pseudovorticity-velocity formulation, are carried out for two- or three-dimensional flow and temperature fields of natural convection in an air-filled vertical enclosure, The enclosure is subjected to differential heating at two vertical sidewalls. The other sidewalls of the enclosure are thermally insulated. The numerical technique employed involves finite difference in the direction normal to the differentially heated walls and pseudospectral approximation in the other two directions normal to the adiabatic walls of the enclosure. The numerical features of the present simulations have been validated by comparing with corresponding results in the literature. The present formulation has been demonstrated to be capable of yielding effectively a divergence-free two- or three-dimensional buoyancy-driven velocity field in the enclosure.