We describe here a collocated finite volume scheme which was recently developed for the numerical simulation of the incompressible Navier-Stokes equations on unstructured meshes, in 2 or 3 space dimensions. We recall its convergence in the case of the linear Stokes equations, and we prove a convergence theorem for the case of the Navier-Stokes equations under the Boussinesq hypothesis. We then present several numerical studies. A comparison between a cluster-type stabilization technique and the more classical Brezzi-Pitkäranta method is performed, the numerical convergence properties are presented on both analytical solutions and benchmark problems and the scheme is finally applied to the study of the natural convection between two eccentric cylinders