A VOF-Based Conservative Interpolation Scheme for Interface Tracking (CISIT) of Two-Fluid Flows

A simple interface-reconstruction scheme (CISIT), based on the volume-of-fluid (VOF) formulation and applicable to unstructured grids with arbitrary topology, is developed to track the interface in free-surface flows. The interface is represented by the contour surface of VOF value f=0.5, which is constructed simply by interpolation. The advancing of the interface is made by imposing mass conservation in the cells containing the interface. However, problems arise when the interface moves across the cell face and into another cell. The cell originally occupied by the interface may be overfilled (f>1) or underfilled (f<1) as the interface advances (moving in the positive direction of the interface) to leave the cell. In contrast, the cell may be overdepleted (f<0) or underdepleted (f>0) as the interface retreats (moving in the negative direction of the interface) to move out of the cell. These situations are remedied via adjusting the transported volume of fluid across the cell face by following the conservation law so that the VOF becomes 1 or 0 in these cells, depending on advancing or retreating of the interface. The resulting VOF distribution is uniform, either in 1 or 0, in the region outside the interface cells, and the interface occupies only one cell in its width. To smooth the fluid properties across the interface region in the velocity calculation, an average smoothing technique is adopted. Application to a number of test cases, including model cases with known velocities and a number of real flows, reveal that this method is accurate and robust.