Level-set computations of free surface rotational flows

A numerical method is developed for modelling the violent motion and fragmentation of an interface between two fluids. The flow field is described through the solution of the Navier-Stokes equations for both fluids (in this case water and air), and the interface is captured by a Level-Set function. Particular attention is given to modelling the interface, where most of the numerical approximations are made. Novel features are that the reinitialization procedure has been redefined in cells crossed by the interface; the mass across the interface has been smoothed using an exponential function to obtain an equally stiff variation of the density and of its inverse; and we have used an Essentially Non-Oscillatory scheme with a limiter whose coefficients depend on the distance function at the interface. The results of the refined scheme have been compared with those of the basic scheme and with other numerical solvers, with favourable results. Besides the case of the vertical surface-piercing plate (for which new laboratory measurements were carried out) the numerical method is applied to problems involving a dam-break and wall-impact, the interaction of a vortex with a free surface, and the deformation of a cylindrical bubble. Promising agreement with other sources of data is found in every case