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.

流行的SPH方法仍然是流体模拟中使用最广泛的方法之一，在最近几十年中它以新的变化形式表现出其长寿性。在仿真高速流体时，此类挑战仍然阻碍了最近几年SPH仿真的新进展。在本文中，我们的研究工作致力于当流体颗粒之间的速度比较大时，SPH模拟的效率问题。具体而言，我们引入一个ķ-在SPH框架中采用均值聚类方法将流体粒子根据其速度动态划分为两个不相交的组。然后，对于这两种类型的粒子，我们使用两级时间步长方案。较小的时间步长用于具有较高速度的粒子，以便保留时间细节并确保稳定性。相反，较大的时间步长用于具有较小速度的粒子以减少计算费用，并且两种类型的粒子在仿真中都紧密耦合。我们进行了各种实验，并将我们的方法与一些最相关的工作进行了比较，这些结果证明了我们的方法在效率和稳定性方面优于常规SPH技术及其新变体的优势。