A comparative study of split advection algorithms on Moment-of-Fluid (MOF) method for incompressible flow

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.