Navier-Stokes calculations with a coupled strongly implicit method. Part 1: Finite-difference solutions

Stone's unconditionally stable, strongly implicit numerical method is extended to the 2x2 coupled vorticity-stream function form of the Navier-Stokes equations. The solution algorithm allows for complete coupling of the boundary conditions. Solutions for arbitrary large time steps, and for cell Reynolds numbers much greater than two have been obtained. The method converges quite rapidly without adding artificial viscosity or the necessity for under relaxation. This technique is used here to solve for a variety of internal and external flow problems. Moderate to large Reynolds numbers are considered for both separated and unseparated flows. The procedure is extended to higher-order splines in Part 2 of this study.