Data from: A computational method for sharp interface advection

We devise a numerical method for passive advection of a surface, such as
the interface between two incompressible fluids, across a computational
mesh. The method is called isoAdvector, and is developed for general
meshes consisting of arbitrary polyhedral cells. The algorithm is based on
the volume of fluid (VOF) idea of calculating the volume of one of the
fluids transported across the mesh faces during a time step. The novelty
of the isoAdvector concept consists in two parts: First, we exploit an
isosurface concept for modelling the interface inside cells in a geometric
surface reconstruction step. Second, from the reconstructed surface, we
model the motion of the face-interface intersection line for a general
polygonal face to obtain the time evolution within a time step of the
submerged face area. Integrating this submerged area over the time step
leads to an accurate estimate for the total volume of fluid transported
across the face. The method was tested on simple 2D and 3D interface
advection problems both on structured and unstructured meshes. The results
are very satisfactory both in terms of volume conservation, boundedness,
surface sharpness, and efficiency. The isoAdvector method was implemented
as an OpenFOAM® extension and is published as open source.