A three-dimensional smoothly adaptive multi-resolution LSMPS method based on power diagram

Mesh-free particle methods possess inherent advantages in modeling large-deformation free-surface and multiphase flows; however, their prohibitive computational costs pose a critical bottleneck on their application in large-scale three-dimensional numerical simulations. To overcome this efficiency limitation while maintaining accuracy, this paper proposes a power diagram-based Smoothly Adaptive Multi-Resolution (AMR) Least Squares Moving Particle Semi-implicit (LSMPS) method. This approach establishes a dual-criteria resolution adaptation mechanism based on the distances to both the free surface and the multiphase interface, enabling simultaneous high-resolution capture of both bubble dynamics and free-surface topology. Critically, a continuous resolution transition strategy is implemented to bridge the high-resolution interface region and the coarse background fluid. This formulation ensures a spatially continuous variation in particle size, effectively suppressing numerical oscillations caused by abrupt resolution jumps. To address the long-standing challenges of topological disorder and conservation violations inherent in traditional AMR techniques, this study develops a particle splitting algorithm utilizing predefined unit sphere templates, alongside a particle splitting and merging algorithm that strictly preserves mass and momentum conservation. Furthermore, numerical stability is significantly enhanced by integrating a particle shifting technique driven by power cell centroids. Validation through three-dimensional benchmark cases—including two-phase hydrostatic, square bubble oscillation, single bubble rising, and double bubble coalescence—demonstrates that this method not only accurately reproduces topological deformations and dynamic characteristics but also furnishes an efficient and robust framework for large-scale multiphase flow simulations.