Numerical simulation of two-phase free surface flows

Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volume-of-fluid method is used for the numerical simulation of two-phase free surface flows involving an incompressible liquid and a compressible gas and taking into account the surface tension effects. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain, while the dynamical effects in the ideal gas are disregarded. A time splitting scheme is used together with a two-grids method for the space discretization. An original algorithm is introduced to track the bubbles of gas trapped in the liquid. Numerical results are presented in the frame of mold filling and bubbles and droplets flows. Some theoretical results concerning free boundary problems are also summarized.