Unstructured pressure-correction solver based on a consistent discretization of the Poisson equation

Abstract

A finite volume incompressible flow solver is presented for three-dimensional unsteady flows based on an unstructured tetrahedral mesh, with collocation of the flow variables at the cell vertices. The solver is based on the pressure-correction method, with an explicit prediction step of the momentum equations followed by a Poisson equation for the correction step to enforce continuity. A consistent discretization of the Poisson equation was found to be essential in obtaining a solution. The correction step was solved with the biconjugate gradient stabilized (Bi-CGSTAB) algorithm coupled with incomplete lower–upper (ILU) preconditioning. Artificial dissipation is used to prevent the formation of instabilities. Flow solutions are presented for a stalling airfoil, vortex shedding past a bridge deck and flow in model alveoli. Copyright © 2000 John Wiley & Sons, Ltd.