Embedded semi-analytical modeling of small scales in simulations of multiphase flow

Multiphase flows are notorious for generating ``features,’’ such as drops, threads and films, much smaller than the dominant interface scales. For small enough scales, surface tension and viscous effects are usually strong so the geometry and the flow are relatively simple and can be described by semi-analytical models. Resolving the smallest scales fully in numerical simulations is expensive and we explore how semi-analytical models can be coupled with fully resolved simulations of the rest of the flow, to reduce the resolution requirement. Small-scale structures are ``collapsed’’ to singularities (points, lines and sheets) by applying filtering to the interface and equations for the evolution of the singularity strength and their coupling with the resolved fluid are derived. The singularities are captured using Lagrangian points advected by the flow, while the rest of the governing equations are solved using a Eulerian approach. The idea and the approach are described and results for simple test cases, as well as preliminary results for a 2D perturbed jet are shown. The results are evaluated by comparison with fully resolved simulations. Low dimensional models such as this one can potentially reduce the computational cost of multiscale and multiphase simulations.