A numerical method for simulating discontinuous shallow flow over an infiltrating surface
A numerical method based on the MacCormack finite difference scheme is presented. The method was developed for simulating two-dimensional overland flow with spatially variable infiltration and microtopography using the hydrodynamic flow equations. The basic MacCormack scheme is enhanced by using the method of fractional steps to simplify application; treating the friction slope, a stiff source term, point-implicitly, plus, for numerical oscillation control and stability, upwinding the convective acceleration term. A higher-order smoothing operator is added to aid oscillation control when simulating flow over highly variable surfaces. Infiltration is simulated with the Green-Ampt model coupled to the surface water component in a manner that allows dynamic interaction. The developed method will also be useful for simulating irrigation, tidal flat and wetland circulation, and floods. Copyright (C) 2000 John Wiley & Sons, Ltd.
finite difference maccormack scheme upwind shallow water equations point-implicit