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

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 te rms of an orthogonal curvilinear co-ordinate system. This approach is in fa ct one kind of the so-called fractional step method that has been popularly used for computations of dynamic flow. By following that the momentum equa tions are decomposed into two portions, the computation procedure involves two steps. The first step (dispersion step) is to compute the provisional v elocity in the momentum equation without the pressure gradient. The second step (propagation step) is to correct the provisional velocity by consideri ng a divergence-free velocity field, including the effect of the pressure g radient. This newly proposed method, other than the conventional split-oper ator methods, such as the projection method, considers the effects of press ure gradient and bed friction in the second step. The advantage of this tre atment is that it increases flexibility, efficiency and applicability of nu merical simulation for various hydraulic problems. Four cases, including ba ck-water flow, reverse flow, circular basin flow and unsteady flow, have be en demonstrated to show the accuracy and practical application of the metho d. Copyright (C) 1999 John Wiley & Sons, Ltd.