VOF (Volume of Fluid) methods can be categoried by the interface reconstruction method. Depending upon the method used in computing the interface normal (slope):

1.One-dimensional (operator split) 2.Multi-dimensional

Question:

What does it mean by one-dim of multi-dim? What is the meaning of the noun "operator split"?

split method means that your reconstruct and advect in one direction say the x direction then you repeat for the other direction say the y direction instead of a multidimensional (or unsplit) method where the advection and reconstruction is done in one step.

A simple split method tends to be more accurate than the unsplit method (if one takes into consideration the directional bias) thus it tends to be more dispersive and one may need to build in a flux limiter to the algorithm.

sorry I think I am babbling now.