1. Introduction
A new VOF advection method based on a 3-D reconstruction of the fluid interface has been developed and implemented in FLOW-3D® Version 8.2. The Volume-of-Fluid (VOF) function is moved in one step, without resorting to an operator splitting technique, which gives the present method increased accuracy when the flow is not aligned with a coordinate direction.
The existing VOF advection method in FLOW-3D® (hereinafter called the standard method) is based on the donor-acceptor approach first introduced by Hirt and Nichols [1]. Numerous enhancements have been made to the original algorithm to improve its accuracy and stability in complex one- and two- fluid flows with sharp interfaces1.
The standard method uses operator splitting and old time-level values of the VOF function to compute fluxes in three coordinate directions. The approach creates a possibility of overfilling or over-emptying computational cells when volume fluxes are significant in all three directions and the time step size is close to the local Courant stability limit.
The new advection method has been developed to alleviate these deficiencies of the standard algorithm. The fluid interface is reconstructed in 3D using a piecewise linear representation, where the interface is assumed to be planar in each control volume (or cell) containing the interface. The fluid volume bounded by the interface and cell faces is then moved according to the local velocity vector in a Lagrangian manner. Finally, the advected volume is overlaid back onto the Eulerian grid to obtain the new values of the fraction-of-fluid function. This combination of the Lagrangian and Eulerian methodology gives the new method its name (similar approaches have been used to approximate advection terms, for example, by Colella [2], Puckett et al [3], and Pilliod and Puckett [4]). The new option is activated in the code by setting IFVOF=5.