Iterative solution of Navier-Stokes dual variable difference equations

Abstract

The dual transformation applied to implicit finite difference approximations of the Navier-Stokes equations reduces the number of unknowns by a factor of three, removes the pressures from the discrete equations and produces velocities which satisfy the discrete continuity equation exactly. New iterative methods for the solution of the unsymmetrical dual variable system are developed and are proven to converge for a large class of problems. These iterative methods involve a sequence of discrete Laplacian systems whose solutions converge to the solution of the dual variable system. They take advantage of the special structure of the dual variable coefficient matrix, are very fast compared to the direct methods currently used, are less memory intensive and can be more easily vectorized and parallelized.