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 theunknown. 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 © 2007 John Wiley & Sons, Ltd.