Abstract
This paper uses a generalization of the SMAC method, which is commonly used to solve incompressible Navier-Stokes equations, to demonstrate that a simultaneous velocity-pressure relaxation algorithm for the HSMAC method is equivalent to a SOR algorithm for a discretized pressure Poisson equation. Two computational algorithms are introduced, each of which uses the conjugate gradient (CG) method for the solution of the pressure Poisson equation. The first uses a simultaneous velocity-pressure relaxation-type CG method ; the second uses a CG method without matrix representation.
