We develop a velocity-pressure algorithm with a pressure Neumann condition in primitive variables using finite differences, for a 2D thermally driven square cavity flow with the Boussinesq approximation and a fixed Prandtl number. The pressure field is updated in a one-step weighted form. Simulations were made for several Rayleigh numbers and the results are close to those found in the literature. © 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.