Improved Normals and Curvatures From 2D Volume Fractions

Among numerous methods for numerical simulation of two-phase flows, e.g. wave impact to marine vessels and ocean structures, the volume-of-fluid (VoF) method is one that can exactly preserve the volume of each phase [4, 5]. In the VoF method, the volume fraction f of one phase is considered as a reference, and defined in each cell as the ratio of the volume occupied by that phase to the total cell volume. Cells with f = 1 and f = 0 are then full of one or the other fluid; those cells with 0 < f < 1 define the interface between the phases. Such a volume fraction field is discontinuous, and so it is difficult to obtain accurate estimates of interface normals and curvatures, required both by the geometric advection algorithms that are typical of VoF methods [6], and for the surface tension term that must be calculated by an accompanying flow solver [2]. Here, we present two new methods for calculating normals and curvatures from volume fractions.