  The moment-of-fluid method (MOF) is known as an extension of the
volume-of-fluid method with piecewise linear interface construction (VOF-PLIC).
In this study, several directional splitting advection algorithms are extended
from the VOF-PLIC method to the MOF method. Those methods, along with some
existing directional splitting algorithms, are presented in detail, especially
on the geometrical and non-geometrical nature of the advection algorithm.
Besides, we also proposed a simple and efficient analytic form to calculate the
volume and centroid of the intersection polyhedron in 3D. Several numerical
tests, including both 2D and 3D tests, are carried out to investigate mass
conservation and geometrical error. Numerical results suggest that the mixed EI
and LE scheme (EILE2D) \citep{aulisa_geometrical_2003} has the best overall
performance in 2D and Weymouth and Yue's scheme (WY) has the best overall
performance in 3D.
