An implicit numerical algorithm for solving non-hydrostatic free-surface flow problems

Details are given of the development of a two-dimensional vertical numerica l model for simulating unsteady free-surface flows, using a non-hydrostatic pressure distribution. In this model, the Reynolds equations and the kinem atic free-surface boundary condition are solved simultaneously, so that the water surface elevation can be integrated into the solution and solved for , together with the velocity and pressure fields. An efficient numerical al gorithm has been developed, deploying implicit parameters similar to those used in the Crank-Nicholson method, and generating a block tri-diagonal alg ebraic system of equations. The model has been applied to simulate a range of unsteady flow problems involving relatively strong vertical acceleration s. The results show that the numerical algorithm described is able to produ ce accurate predictions and is also easy to apply. Copyright (C) 2001 John Wiley & Sons, Ltd.