A Conservative Hybrid Eulerian-Lagrangian Method with Persistent Structure Tracking for Multiscale Cavitation

Hybrid Eulerian-Lagrangian methods for multiscale cavitation represent grid-resolved vapor structures in an Eulerian mixture formulation and unresolved bubbles in a Lagrangian description, necessitating transitions between the two representations as structures evolve. Conventional approaches address these transitions as local geometric operations, lacking the ability to utilize structure history, leading to ambiguity in event detection and execution. This work introduces a conservative hybrid framework with a persistent structure-tracking methodology, employing connected-component labeling for resolved vapor structures, which maintains persistent identities and histories throughout the simulation. The methodology incorporates physics-informed prediction for structure positions and sizes to support the initialization of newly formed Lagrangian bubbles. Additionally, it derives conservative transfer operators for vapor mass and momentum preservation. Canonical verification cases validate this framework's capability for persistent identity preservation during dynamic events like fragmentation and coalescence and demonstrate its robustness in parallel computation environments. The proposed methodology ultimately enhances the numerical treatment of cavitation dynamics by offering a reliable and history-aware transition mechanism.