A Hybrid Lagrangian-Eulerian Method (hLE) for Interface Tracking

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. The approach uses marker points around the interface and advects the signed distance to the interface in a Lagrangian frame. The kernel–based derivative calculations typical of particle methods are used to extract the interface normal and curvature from unordered marker points. Connectivity between the marker points is not necessary. The fluid flow equations are solved on a background, fixed mesh using a co-located grid finite volume solver together with balanced force algorithm (Francois et al. JCP, 2006, Herrmann JCP, 2007) for surface tension force. The numerical scheme is first validated for standard test cases: (i) parasitic currents in a stationary spherical drop, (ii) small amplitude damped surface waves, (iii) capillary waves on droplet surface, (iv) RayleighTaylor instability, and (v) gravity-driven bubble/droplet in a stationary fluid. Extension of the approach to three-dimensions is conceptually straight forward, however, poses challenges for parallel implementation. A domain-decomposition based on balancing the number of grid points per processor gives rise to load– imbalance due to uneven distribution of the marker points and advanced domain partitioning methods are needed for improved efficiency of the approach. ∗Corresponding Author: [email protected]