Robust and efficient SPH simulation for high-speed fluids with the dynamic particle partitioning method

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, we then 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 the numerical stability. In contrast, the larger time steps are used for particles with smaller speeds to reduce the computational expense, and both types of particles are tightly coupled in the simulation. We conduct various experiments which have manifested the advantages of our methods over the conventional SPH technique and its new variants in terms of efficiency and stability.