Projection method for viscous incompressible flow on quadrilateral grids

Abstract

This paper describes a second-order projection method for the incompressible Navier-Stokes equations on multiply connected domains with a logically rectangular quadrilateral grid. The method uses a second-order fractional step scheme in which one first solves diffusion-convection equations to determine intermediate velocities which are then projected onto the space of divergence-fr ee vector fields. The spatial discretizations are accomplished by formally transforming the equations to a computational space with a uniform grid. The diffusion, pressure gradient, and divergence terms are 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. Numerical results are presented illustrating the performance of the method.