The subject of this book is the development of an efficient numerical method capable of predicting the flow behavior of two-phase immiscible fluids. In the quest of an accurate and robust numerical method for the modeling of two-phase flows, one has to keep in mind the intrinsic properties and difficulties associated with the problem: (i) those flows are mostly three-dimensional, (ii) the interface might encounter a lot of topology changes, (iii) large jumps of density and viscosity might exist across the interface, (iv) surface tension forces may play a very important role in the interface...