Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry

We present and analyse two new Volume-of-Fluid (VOF) reconstruction algorithms that approximate the interface separating two immiscible fluids as a linear function in each grid cell (PLIC Piecewise Linear Interface Calculation). The first one is based on two simple geometrical criteria for the reconstruction of a linear interface, the second one minimizes a distance functional to find the plane coefficients. Their performance is tested for several smooth surfaces. The geometrical nature of operator split advection is quicklyreviewed and a new three-dimensional split advection algorithm is presented. It is exactly mass conserving for a divergence-free velocity field and its accuracy rapidly increases as the CFL number is decreased. Secondorder convergence is found in the case of velocity fields with not uniform vorticity at high grid resolutions in the asymptotic regime.