A three-dimensional non-hydrostatic vertical boundary fitted model for free-surface flows

A non-hydrostatic finite volume model is presented to simulate three-dimensional (3D) free-surface flows on a vertical boundary fitted grid system. The algorithm, which is an extension to the previous two dimensional vertical (2DV) model proposed by Ahmadi et al. (Int. J. Numer. Meth. Fluids 2007; 54(9):1055-1074), solves the complete 3D Navier-Stokes equations in two major steps based on projection method. First, by excluding the pressure terms in momentum equations, a set of advection-diffusion equations are obtained. In the second step, the continuity and the momentum equations with the remaining pressure terms are solved which yields a block tri-diagonal system of equations with pressure as the unknown. In this step, the 3D system is decomposed into a series of 2DV plane sub-systems which are solved individually by a direct matrix solver. Iteration is required to ensure convergence of global 3D system. To minimize the number of vertical layers and subsequently the computational cost, a new top-layer pressure treatment is proposed which enables the model to simulate a range of surface waves using only 2-5 vertical layers. Copyright (C) 2007 John Wiley & Sons, Ltd.