A finite volume method to solve the Navier-Stokes equations for incompressible flows on unstructured meshes

A method to solve the Navier-Stokes equations for incompressible viscous flows and the convection and diffusion of a scalar is proposed in the present paper. This method is based upon a fractional time step scheme and the finite volume method on unstructured meshes. A recently proposed diffusion scheme with interesting theoretical and numerical properties is tested and integrated into the Navier-Stokes solver. Predictions of Poiseuille flows, backward-facing step flows and lid-driven cavity flows are then performed to validate the method. We finally demonstrate the versatility of the method by predicting buoyancy force driven flows of a Boussinesq fluid (natural convection of air in a square cavity with Rayleigh numbers of 10(3) and 10(6)). (C) 2000 Editions scientifiques et medicales Elsevier SAS.