Use of two-step split-operator approach for 2D shallow water flow computation

Abstract

The objective of this paper is to present a methodology of using a two-step split-operator approach for solving the shallow water flow equations in terms of an orthogonal curvilinear co-ordinate system. This approach is in fact one kind of the so-called fractional step method that has been popularly used for computations of dynamic flow. By following that the momentum equations are decomposed into two portions, the computation procedure involves two steps. The first step (dispersion step) is to compute the provisional velocity in the momentum equation without the pressure gradient. The second step (propagation step) is to correct the provisional velocity by considering a divergence-free velocity field, including the effect of the pressure gradient. This newly proposed method, other than the conventional split-operator methods, such as the projection method, considers the effects of pressure gradient and bed friction in the second step. The advantage of this treatment is that it increases flexibility, efficiency and applicability of numerical simulation for various hydraulic problems. Four cases, including back-water flow, reverse flow, circular basin flow and unsteady flow, have been demonstrated to show the accuracy and practical application of the method. Copyright (C) 1999 John Wiley & Sons, Ltd.