Volume of fluid method

The volume of fluid method, often abbreviated VOF, is a family of numerical techniques in computational fluid dynamics for tracking and locating a free surface, the boundary between two fluids such as water and air. It belongs to the Eulerian methods, in which the mesh is fixed or moves in a prescribed way, and it is an advection scheme that captures the shape and position of the interface rather than a complete flow solver, so the Navier-Stokes equations must be solved separately. Instead of the many marker particles used by the earlier marker-and-cell method developed at Los Alamos National Laboratory, VOF stores one scalar per grid cell, the fraction of the cell filled by the tracked fluid: zero for an empty cell, one for a full cell and a value in between where the interface passes. That fraction is moved by a transport equation, and fluid properties such as density are averaged by volume fraction so that all fluids share one momentum equation. The approach was first demonstrated in 1975 by Nichols and Hirt, the name was coined in a 1980 Los Alamos report on the SOLA-VOF program, and Youngs added the piecewise-linear interface calculation in 1982. VOF needs little storage and copes with the merging and breakup of fluid regions, but its main difficulty is smearing of the interface, which donor-acceptor schemes, higher-order differencing and geometric line reconstruction each try to limit.