A collocated finite volume scheme to solve free convection for general non-conforming grids

We present a new collocated numerical scheme for the approximation of the Navier–Stokes and energy equations under the Boussinesq assumption for general grids, using the velocity–pressure unknowns. This scheme is based on a recent scheme for the diffusion terms. Stability properties are drawn from particular choices for the pressure gradient and the non-linear terms. Convergence of the approximate solutions may be proven mathematically. Numerical results show the accuracy of the scheme on irregular grids.