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.