A reduced implicit scheme, via discrete stream function generation, for unsteady Navier-Stokes equations in general curvilinear coordinates.

finite difference method, based on the generation of a discrete stream function, is proposed for the solution of unsteady incompressible viscous flows. The discrete stream function is obtained by operating as at the continuum level, but directly on the discretized form of the Navier Stokes equations. The resulting numerical procedure allows the boundary conditions to be given in primitive variables and, at the same time, produces a set of velocities which exactly satisfy the mass conservation in discretized form, by eliminating the pressure as a variable to be computed. These features of the method are very useful for free surface unsteady problems. For this purpose the extension of the method to curvilinear moving grids is outlined. The general properties of the method in comparison with others based on the continuum stream function are discussed and illustrated with some computational results.