VOF method

It is a surface-tracking technique applied to a fixed Eulerian mesh where the Navier Stokes equations which describe the motion of the flow have to be solved separately.
 
The method is based on the solution of a transport equation for variable ‘C’ (often also referred as indicator or color function) for the liquid phase.
 
                                              
Cij represents the portion of the area of the cell (i, j) filled with liquid phase  and the phase function χ :
                       
We have 0 < C < 1 in cells cut by the interface S and C = 0 or 1 away from it.
 

The VOF method doesn't explicitly track the interface, it reconstructs the interface based on calculate the volume fraction of fluid . The Color Function also cannot be solved easily. There are already several method to approach, different approach gives different accuracy,  the most popular is PLIC (Piecewise Linear Interface Calculate). In a 3D space, the interface can be described by nx+ny+nz=a.

nx+ny+nz