Interface reconstruction with least-square fit and split Eulerian-Lagrangian advection

Two new volume-of-fluid (VOF) reconstruction algorithms, which are based on a least-square fit technique, are presented. Their performance is tested for several standard shapes and is compared to a few other VOF/PLIC reconstruction techniques, showing in general a better convergence rate. The geometric nature of Lagrangian and Eulerian split advection algorithms is investigated in detail and a new mixed split Eulerian implicit-Lagrangian explicit (EI-LE) scheme is presented. This method conserves the mass to machine error, performs better than split Eulerian and Lagrangian algorithms, and it is only slightly worse than unsplit schemes. However, the combination of the interface reconstruction with the least-square fit and its advection with the EI-LE scheme appears superior to other existing approaches.