  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(R) extension and is published as open source.
