This paper describes a three-dimensional finite volume method for the prediction of supercritical fluid buoyant flows in heated enclosures. The space and the time accuracies of the method are checked on an exact analytical solution, and the solver is validated for several benchmark tests for natural convection inside a differentially heated cavity both in the Boussinesq and in the low Mach number approximations. Then, the influence of the linearization of the van der Waals equation of state on the global convergence is discussed. Comparisons, based on the Rayleigh number, between the supercritical fluid and the perfect gas flows in a side heated cavity, show many similarities in the thermal equilibria and considerable differences in the transient behaviours.