Multidimensional Free Surface Detection in Smoothed Particle Hydrodynamics

ABSTRACT This paper presents a multidimensional free‐surface detection method for Smoothed Particle Hydrodynamics (SPH) simulations aimed at highly dynamic flows. The approach combines density‐guided candidate selection with an efficient seed‐and‐expand strategy: outermost‐particle seeding is followed by breadth‐first search (BFS) refinement, while local surface normal estimated via principal component analysis (PCA) guide adaptive sector/cone scanning to improve robustness in high‐curvature and fragmented interfaces. To accelerate neighborhood queries, the method employs dimension‐dependent spatial indexing (hash grids in 2D and an octree in 3D), reducing the practical cost of neighbor search compared with exhaustive scanning. The framework is validated on benchmark cases including 2D/3D tank sloshing and a 3D dam‐break scenario. Results show improved interface identification accuracy over a standard density‐ratio baseline (e.g., 12.7% higher interfacial precision in our tests) and substantially faster neighborhood‐query performance (up to 72% reduction in the query stage), enabling reliable near–real‐time free‐surface detection for large‐scale SPH simulations.