A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

This paper is concerned with the numerical solutions of time dependent two‐dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier–Stokes and mass conservation equations are solved by a semi‐implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non‐linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110:171–186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199–210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die‐swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions.