A level set technique applied to unsteady free surface flows

An unsteady Navier-Stokes solver for incompressible fluid is coupled with a level set approach to describe free surface motions. The two-phase now of air and water is approximated by the flow of a single fluid whose propertie s, such as density and viscosity, change across the interface. The free sur face location is captured as the zero level of a distance function convecte d by the flow field. To validate the numerical procedure, two classical two -dimensional free surface problems in hydrodynamics, namely the oscillating flow in a tank and the waves generated by the flow over a bottom bump, are studied in non-breaking conditions, and the results are compared with thos e obtained with other numerical approaches. To check the capability of the method in dealing with complex free surface configurations, the breaking re gime produced by the flow over a high bump is analyzed. The analysis covers the successive stages of the breaking phenomenon: the steep wave evolution , the falling jet, the splash-up and the air entrainment. In all phases, nu merical results qualitatively agree with the experimental observations. Fin ally, to investigate a flow in which viscous effects are relevant, the nume rical scheme is applied to study the wavy flow past a submerged hydrofoil. Copyright (C) 2001 John Wiley & Sons, Ltd.