Numerical simulation of 3D quasi-hydrostatic, free-surface flows

Numerical models that assume hydrostatic pressure are usually sufficiently accurate for applications in civil engineering where the vertical component of the velocity is relatively small. Nevertheless, the vertical momentum, and, hence, the nonhydrostatic pressure component, cannot be neglected when the bottom topography of the domain changes abruptly as in cases of short waves, or when the flow is determined by strong density gradients. In this paper a numerical method for the three-dimensional (3D) quasi-hydrostatic, free-surface flows is outlined. The governing equations are the Reynolds-averaged Navier-Stokes equations with the pressure decomposed into the sum of a hydrostatic component and a hydrodynamic component. The momentum equations, the incompressibility condition, and the equation for the free surface are integrated by a time-splitting method in such a fashion that the resulting numerical solution is mass conservative and stable at a minimal computational cost. Several applications serve to illustrate the effect of the deviation from the hydrostatic pressure.