Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem. We introduce particle merging-and-splitting, a simple scheme for robustly handling collisions between particles that prevents inter-penetrations of separate objects without introducing numerical instabilities. This scheme merges colliding particles at the beginning of the time-step and then splits them at the end of the time-step. Thus, collisions last for the duration of a time-step, allowing neighboring particles of the colliding particles to influence each other. We show that our merging-and-splitting method is effective in robustly handling collisions and avoiding penetrations in particle-based simulations. We also show how our merging-and-splitting approach can be used for coupling different simulation systems using different and otherwise incompatible integrators. We present simulation tests involving complex solid-fluid interactions, including solid fractures generated by fluid interactions.

中文翻译：

---

粒子合并与分裂

在基于粒子的大型模拟中稳健地处理单个粒子之间的碰撞一直是一个具有挑战性的问题。我们引入了粒子合并和分裂，这是一个简单的方案，用于稳健地处理粒子之间的碰撞，防止单独对象的相互渗透，而不会引入数值不稳定性。该方案在时间步开始时合并碰撞粒子，然后在时间步结束时将它们分开。因此，碰撞持续一个时间步长的持续时间，允许碰撞粒子的相邻粒子相互影响。我们表明，我们的合并和分裂方法在稳健地处理碰撞和避免基于粒子的模拟中的穿透方面是有效的。我们还展示了我们的合并和拆分方法如何用于耦合使用不同且不兼容的积分器的不同仿真系统。我们提出了涉及复杂固液相互作用的模拟测试，包括由流体相互作用产生的固体裂缝。