A modified volume of fluid advection method for uniform Cartesian grids

This paper presents a modification on the stair-shaped volume of fluid (VOF) advection algorithm called defined donating and accepting region (DDAR) scheme which shows the importance of the more accurate definition of donating and accepting region. The algorithm which is suitable for uniform Cartesian grids uses multi-dimensional method of cell boundary flux integration. The performance of the modified scheme presented here has been compared with the performance of a number of alternative schemes taking into account translation, rotation and shear advection tests. In some aspects, the DDAR scheme is shown to be more accurate than linear constant and flux limited schemes, and in some way comparable with the linear piecewise schemes (PLIC). Without using any geometrical information, DDAR scheme predicts flux correctly using information of cell volume fraction and its face velocities and consequently improves the performance the first order DDR schemes.