A simple and conservative operator-splitting semi-Lagrangian volume-of-fluid advection scheme

A semi-Lagrangian, operator-splitting, high-performance volume-of-fluid advection scheme (SLOSH-VOF) is developed. In the backward time integration a directional splitting strategy is adopted, which greatly simplifies the definition and locating of the departure volume and reduces it to a grid cell expanded or compressed in one grid direction. The VOF value in the departure cell is estimated using a geometrical interpolation algorithm with a piecewise linear interface calculation (PLIC) scheme for the interfacial cells. The proposed SLOSH-VOF method is unconditionally stable and very large time steps can be used to significantly speed up the overall computations. It is conceptually simple and can be very easily implemented due to the direction-split advection. Its performance is evaluated through several benchmark advection tests. The SLOSH-VOF results are comparable to those from an Eulerian VOF method in terms of interface position errors, and improved with regard to mass conservation, even with CFL numbers increased up to one order of magnitude.