An improved scheme for the interface reconstruction and curvature approximation for flow simulations of two immiscible fluids

A new scheme is proposed for the approximation of the curvature field in the context of two-phase flows. Direct computation of the curvature from the volume fraction distribution produces so-called spurious currents, which are numerical non-physical velocities especially in the vicinity of the interface. The proposed method computes the curvature from the signed distance function. We have implemented the method inside Open FOAM® framework (an open source C++ toolbox for computational fluid dynamics simulations based on finite volume discretization). The surface tension force has been formulated into the sharp surface force (SSF). The implementation is applicable for general mesh topologies (two or three dimensional polyhedra). Different validation test cases have been performed; static air bubble in water, droplet undergoing linear shear, rising bubble into viscous fluid, and the impact of a viscous droplet on a thin cylindrical fiber. The proposed method shows an accurate calculation of the curvature and a significant reduction of spurious currents by several orders of magnitude. Such reduction of spurious currents allows accurate simulations of surface tension dominated flows such as micro-droplets, or liquid-liquid separation.