A second-order projection method for the incompressible Navier Stokes equations on quadrilateral grids

Abstract

This paper describes a second-order projection method for the incompressible Navier-Stokes equations on a logically-rectangular quadrilateral grid. The method uses a second-order fractional step scheme in which one first solves diffusion-convection equations to predict intermediate velocities which are then projected onto the space of divergence-free vector fields. The spatial discretization of the diffusion-convection equations is accomplished by formally transforming the equations to a uniform computational space. The diffusion terms are then discretized using standard finite-difference approximations. The convection terms are discretized using a second-order Godunov method that provides a robust discretization of these terms at high Reynolds number. The projection is approximated using a Galerkin procedure that uses a local basis for discretely divergence-free vector fields. Numerical results are presented illustrating the performance of the method. 13 refs., 5 figs.