PROJECTION METHOD FOR VISCOUS INCOMPRESSIBLE-FLOW ON QUADRILATERAL GRIDS

This paper describes a second-order projection method for the incompre ssible Navier-Stokes equations on multiply connected domains with a lo gically 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 project ed onto the space of divergence-free vector fields. The spatial discre tizations are accomplished by formally transforming the equations to a computational space with a uniform grid. The diffusion, pressure grad ient, and divergence terms are discretized using standard finite diffe rence approximations. The convection terms are discretized using a sec ond-order Godunov method that provides a robust discretization of thes e terms at high Reynolds number. Numerical results are presented illus trating the performance of the method.