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 flow of air and water is approximated by the flow of a single fluid whose properties, such as density and viscosity, change across the interface. The free surface location is captured as the zero level of a distance function convected 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 those obtained with other numerical approaches. To check the capability of the method in dealing with complex free surface configurations, the breaking regime 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, numerical results qualitatively agree with the experimental observations. Finally, to investigate a flow in which viscous effects are relevant, the numerical scheme is applied to study the wavy flow past a submerged hydrofoil.