Three-dimensional numerical modelling of free surface flows with non-hydrostatic pressure

A three-dimensional numerical model is developed for incompressible free surface flows. The model is based on the unsteady Reynolds-averaged Navier-Stokes equations with a non-hydrostatic pressure distribution being incorporated in the model. The governing equations are solved in the conventional sigma co-ordinate system, with a semi-implicit time discretization. A fractional step method is used to enable the pressure to be decomposed into its hydrostatic and hydrodynamic components. At every time step one five-diagonal system of equations is solved to compute the water elevations and then the hydrodynamic pressure is determined from a pressure Poisson equation. The model is applied to three examples to simulate unsteady free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field. Emphasis is focused on applying the model to wave problems. Two of the examples are about modelling small amplitude waves where the hydrostatic approximation and long wave theory are not valid. The other example is the wind-induced circulation in a closed basin. The numerical solutions are compared with the available analytical solutions for small amplitude wave theory and very good agreement is obtained. Copyright (C) 2002 John Wiley Sons, Ltd.