Tensile instability is one of the major obstacles to particle methods in fluid simulation, which would cause particles to clump in pairs under tension and prevent fluid simulation to generate small-scale thin features. To address this issue, previous particle methods either use a background pressure or a finite difference scheme to alleviate the particle clustering artifacts, yet still fail to produce small-scale thin features in free-surface flows. In this article, we propose a dual-particle approach for simulating incompressible fluids. Our approach involves incorporating supplementary virtual particles designed to capture and store particle pressures. These pressure samples undergo systematic redistribution at each time step, grounded in the initial positions of the fluid particles. By doing so, we effectively reduce tensile instability in standard SPH by narrowing down the unstable regions for particles experiencing tensile stress. As a result, we can accurately simulate free-surface flows with rich small-scale thin features, such as droplets, streamlines, and sheets, as demonstrated by experimental results.

拉伸不稳定性是粒子方法在流体模拟中的主要障碍之一，它会导致粒子在张力下成对聚集，并妨碍流体模拟生成小尺度的薄特征。为了解决这个问题，以前的粒子方法要么使用背景压力或有限差分方案来减轻粒子聚类伪影，但仍然无法在自由表面流中产生小尺度薄特征。在本文中，我们提出了一种模拟不可压缩流体的双粒子方法。我们的方法涉及合并旨在捕获和存储粒子压力的补充虚拟粒子。这些压力样本在每个时间步骤都会经历系统的重新分布，以流体粒子的初始位置为基础。通过这样做，我们通过缩小经历拉伸应力的颗粒的不稳定区域来有效地降低标准 SPH 中的拉伸不稳定性。因此，正如实验结果所证明的那样，我们可以准确地模拟具有丰富的小尺度薄特征的自由表面流，例如液滴、流线和片状物。