  A novel interface reconstruction strategy for volume of fluid (VOF) methods
is introduced that represents the liquid-gas interface as two planes that
co-exist within a single computational cell. In comparison to the piecewise
linear interface calculation (PLIC), this new algorithm greatly improves the
accuracy of the reconstruction, in particular when dealing with thin structures
such as films. The placement of the two planes requires the solution of a
non-linear optimization problem in six dimensions, which has the potential to
be overly expensive. An efficient solution to this optimization problem is
presented here that exploits two key ideas: an algorithm for extracting
multiple plane orientations from transported surface data, and an efficient and
mass-conserving distance-finding algorithm that accounts for two planes with
arbitrary orientation. Additionally, a simple and robust strategy is presented
to accurately represent the surface tension forces produced at the interface of
subgrid-thickness films. The performance of this new VOF reconstruction is
demonstrated on several test cases that illustrate the capability to handle
arbitrarily thin films.
