Volume of fluid method
They belong to the class of Eulerian methods which are characterized by a mesh that is either stationary or is moving in a certain prescribed manner to accommodate the evolving shape of the interface.
As such, VOF methods are advection schemes capturing the shape and position of the interface, but are not standalone flow solving algorithms.
MAC used Lagrangian marker particles to track the distribution of fluid in a fixed Eulerian grid.
The original idea of the VOF method was to replace marker particles with a single scalar variable per grid cell representing the volume fraction of fluid in it.
[3] The VOF approach was first demonstrated in a 1975 publication “Methods for Calculating Multi-Dimensional, Transient Free Surface Flows Past Bodies” by Nichols and Hirt.
In 1976, Noh & Woodward[5] presented the Simple Line Interface Calculation (SLIC), a technique to approximate fluid interfaces based on volume fractions, designed for directional-split advection scheme of volume fractions.
SLIC could also handle an arbitrary number of immiscible fluid phases per grid cells.
Thereby, SLIC was well suited to the VOF approach, although the two methods were initially independent and remained separate till the 90s.
The term “Volume of Fluid method” and it acronym “VOF” method were coined in the 1980 Los Alamos Scientific Laboratory report, “SOLA-VOF: A Solution Algorithm for Transient Fluid Flow with Multiple Free Boundaries,” by Nichols, Hirt and Hotchkiss[6] and in the journal publication “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries” by Hirt and Nichols in 1981.
Since VOF method surpassed MAC by lowering computer storage requirements, it quickly became popular.
Early applications of the SOLA-VOF program developed at Los Alamos include light-water-reactor safety studies.
is a discontinuous function insofar as its value jumps from 0 to 1 when the local point moves from the non-tracked to the tracked phase.
The VOF method is computationally friendly, as it introduces only one additional equation and thus requires minimal storage.
The method is also characterized by its capability of dealing with highly non-linear problems in which the free-surface experiences sharp topological changes.
The different methods for treating VOF can be roughly divided into three categories, namely the donor-acceptor formulation, higher order differencing schemes and line techniques.
In his original work, Hirt treated this with a blended scheme consisting of controlled downwinding and upwind differencing.
Such methods include the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) [16] and High Resolution Interface Capturing (HRIC) [17] scheme, which are both based on the Normalized Variable Diagram (NVD) by Leonard.
[18] Line techniques circumvent the problems associated with the discretization of the transport equation by not tracking the interface in a cell explicitly.
In each cell the interface is approximated as a line parallel to one of the coordinate axes and assumes different fluid configurations for the horizontal and vertical movements respectively.
Components of the normal are found e.g. by using the finite difference method or its combination with least squares optimization.
is then found (analytically or by approximation) by enforcing mass conservation within computational cell.
between grid cells, or advecting the endpoints of interface using discrete values of fluid velocity.
In two-phase flows in which the properties of the two phases are vastly different, errors in the computation of the surface tension force at the interface cause Front-Capturing methods such as Volume of Fluid (VOF) and Level-Set method (LS) to develop interfacial spurious currents.
