A sub-grid surface dynamics model for sub-filter surface tension induced interface dynamics

This paper presents a novel model for the sub-filter surface tension induced motion of interfaces separating immiscible fluids. A key feature of the proposed Sub-Grid Surface Dynamics (SGSD) model is to take the sub-filter interface dynamics fully into account by employing a dual-scale approach. Instead of modeling the sub-filter interface geometry, it is resolved on an auxiliary grid using the Refined Level Set Grid approach. The required sub-filter velocity field on the auxiliary grid is reconstructed solving a PDE in a narrow band surrounding the interface. With the fully resolved interface geometry available, the previously unclosed surface tension term in the filtered Navier-Stokes equations can be directly closed using explicit filtering. The novel model shows excellent results for different test cases, including sub-grid oscillations of drops, the sub-grid Rayleigh-Plateau instability, and the viscous capillary breakup of a ligament.