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.