A Hybrid Lagrangian-Eulerian Approach for Two-Phase Flows with Fully Resolved Interfaces

A hybrid Lagrangian-Eulerian (hLE) scheme, combining a particle-based, mesh-free technique with a finitevolume flow solver, is developed for direct simulations of two-phase flows. This approach merges the naturally adaptive nature of particle-based schemes, for efficient representation of the interface between two media, with the relative flexibility offered by grid-based solvers for complex flows. A mesh-free, particle-based scheme for interface tracking (Hieber & Koumoutsakos 2005) is first integrated with a co-located grid based finite volume solver. A balanced force algorithm (Francois et al. 2006, Herrmann 2006), for accurate representation of surface tension forces, is used to solve the two-phase flow equations on a fixed background mesh. The accuracy of the particle-based scheme is first verified for standard test cases on interface tracking. The hybrid scheme is then applied to perform coupled two-phase flow simulations of stationary drop and rising bubbles. ∗Corresponding Author: [email protected]