Coupling a VOF method and an interface normal transport equation for two-phase flow

In a direct numerical simulation (DNS) of two-phase flows many techniques, such as the Volume-of-Fluid (VOF), surface markers and the level set methods, have been used to track the evolution of a line or a surface. These methods have been successfully applied to industrial and natural flows such as sea waves, jet atomization, splashes, droplet/bubble oscillations which involve breakup and coalescence. In direct numerical simulations the local interface normal vector and curvature are needed to compute the capillary force. These geometrical quantities are usually calculated from the spatial derivatives of a scalar function at any instant in time. A new methodology for calculating the interface normal vector is here proposed. The normals are advected along the streamlines together with the volume fraction data in order to reconstruct more accurately the interface.The accuracy and performance of the new method are demonstrated via standard test cases with a prescribed velocity field and the results are compared with those of traditional VOF methods.