1- Volume of fluid (VOF)

The VOF formulation relies on the fact that two or more fluids. For each phase considered in the model a variable is introduced as the volume fraction of the phase in the computational cell. In each of the control volumes, the volume fractions of all phases sum up to unity. 

2- Level set

The level set method (Sethian, 1999) is a method for implicit description of moving fronts. The basic idea is that the front location is given as the zero level set of an auxiliary field defined over the domain of interest.