Two-phase Impulse Fluid on Particle Flow Map

We present a novel particle flow map framework for the high-fidelity simulation of complex two-phase flows. Our method is built upon a unified Lagrangian formulation in which a shared flow map jointly governs the phase interface evolution and the underlying fluid dynamics. For interface tracking, our particles drive a particle-flow-map-based level set equipped with a hybrid reinitialization strategy, effectively preserving sub-grid geometric features while ensuring robust topological stability. For two-phase dynamics, we introduce an impulse-based solver that reformulates the impulse path integration to depend solely on the continuous velocity field, enabling efficient and accurate handling of interfacial discontinuities without artificial smoothing. By leveraging the particle flow map's inherently low-dissipation tracking of both geometry and dynamics, our framework achieves enhanced geometric accuracy and physical fidelity relative to existing two-phase solvers. Our framework faithfully captures the intricate interplay between intense vortical motion and complex interface geometry, as evidenced by the reproduction of a broad range of challenging phenomena, including interacting bubble rings, breaking waves, and whirlpool drainage.