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ALGORITHMS FOR PRESSURE CORRECTION IN THE DRIVEN CAVITY PROBLEM

Abstract. The driven cavity problem has been extensively used as a benchmark problem to evaluate numerical techniques that solve the Navier-Stokes equations. In this work, the incompressible fluid flow is integrated by calculating the velocity fields and computing the pressure field in each time step. In order to avoid approximation errors, that imply a lack of incompressibility, a dilatation term is incorporated to the Poisson equation of the pressure. The goal of this paper is twofold. The first purpose is to examinate the performance of the three different methods for the pressure correction: the Claeyssen-Bravo algorithm, the iterative scheme given in C. Hirsch (1990), and the steady state solution of the nonhomogeneous diffusion equation. The second goal is to perform numerical experimentation with deep and shallow cavities.