Simulation of free-surface flows by a finite element interface capturing technique

Transient free-surface (FS) flows are numerically simulated by a finite element interface capturing method based on a level set approach. The methodology consists of the solution of two-fluid viscous incompressible flows for a single domain, where the liquid phase is identified by the positive values of the level set function, the gaseous phase by negative ones, and the FS by the zero level set. The numerical solution at each time step is performed in three stages: (i) a two-fluid Navier–Stokes stage, (ii) an advection stage for the transport of the level set function and (iii) a bounded reinitialisation with continuous penalisation stage for keeping smoothness of the level set function. The proposed procedure, and particularly the renormalisation stage, is evaluated in three typical two- and three-dimensional problems.