A time-splitting method for the three-dimensional shallow water equations

In this paper we describe a time-splitting method for the three-dimensional shallow water equations. The stability of this method neither depends on the vertical diffusion term nor on the terms describing the propagation of the surface waves. The method consists of two stages and requires the solution of a sequence of linear systems. For the solution of these systems we apply a Jacobi-type iteration method and a conjugate gradient iteration method. The performance of both methods is accelerated by a technique based on smoothing. The resulting method is mass-conservative and efficient on vector and parallel computers. The accuracy, stability and computational efficiency of this method are demonstrated for wind-induced problems in a rectangular basin.