Dynamic particle partitioning SPH model for high-speed fluids simulation

The popular SPH method still remains as one of the most widely-used methods in fluid simulation, exhibiting its longevity with new and diverse variants in recent decades. New progress in the SPH simulation in most recent years are still hampered by such challenge when simulating high-speed fluids. In this paper, our research efforts are devoted to the efficiency issue of the SPH simulation when the ratio of velocities among fluid particles is large. Specifically, we introduce a k-means clustering method into the SPH framework to dynamically partition fluid particles into two disjoint groups based on their velocities. Then, we use a two-scale time-step scheme for these two types of particles. The smaller time steps are for particles with higher speed in order to preserve temporal details and guarantee stability. In contrast, the larger time steps are used for particles with smaller speed to reduce the computational expense, and both types of particles are tightly coupled in the simulation. We conduct various experiments and compare our method with some of the most relevant works, which have manifested the advantages of our methods over the conventional SPH technique and its new variants in terms of efficiency and stability.