A Hybrid Lagrangian-Eulerian Formulation for Bubble Generation and Dynamics

Abstract: We present a hybrid Lagrangian-Eulerian framework for simulating both small and large scale bubble dynamics, where the bubbles can grow or shrink in volume as dictated by pressure forces in the surrounding fluid. Small under-resolved bubbles are evolved using Lagrangian particles that are monolithically two-way coupled to the surrounding flow in a manner that closely approximates the analytic bubble oscillation frequency while converging to the analytic volume as predicted by the well-known Rayleigh-Plesset equation. We present a novel scheme for interconverting between these under-resolved Lagrangian bubbles and larger well-resolved bubbles that are modeled with a traditional Eulerian level set approach. We also present a novel seeding mechanism to realistically generate bubbles when simulating fluid structure interaction with complex objects such as ship propellers. Moreover, our framework for bubble generation is general enough to be incorporated into all grid-based as well as particle-based fluid simulation methods.