标题： 流体模拟在涡流粒子流场图上 显示英文标题

标题： Fluid Simulation on Vortex Particle Flow Maps

摘要： 我们提出了涡流粒子流图（VPFM）方法来模拟不可压缩流体在动态固体边界存在时复杂的涡旋演化。 我们的方法的核心见解是，涡度是粒子流图上进化的理想量，与速度或动量等其他流体量相比，能够实现显著更长的流图距离。 为了实现这一目标，我们开发了一种混合欧拉-拉格朗日表示法，该表示法在涡流粒子上演化涡度和流图量，同时在背景网格上重建速度。 该方法集成了三个关键组件：(1) 基于涡度的粒子流图框架，(2) 粒子上的精确 Hessian 进化方案，以及 (3) 在 VPFM 中处理固体边界的无穿透和无滑移条件。 这些组件共同使得流图长度比最先进的方法长 3 到 12 倍，增强了在扩展时空域内的涡度保存能力。 我们通过多样化的模拟验证了 VPFM 的性能，展示了其在捕捉复杂涡旋动力学和湍流现象方面的有效性。 显示英文摘要

摘要： We propose the Vortex Particle Flow Map (VPFM) method to simulate incompressible flow with complex vortical evolution in the presence of dynamic solid boundaries. The core insight of our approach is that vorticity is an ideal quantity for evolution on particle flow maps, enabling significantly longer flow map distances compared to other fluid quantities like velocity or impulse. To achieve this goal, we developed a hybrid Eulerian-Lagrangian representation that evolves vorticity and flow map quantities on vortex particles, while reconstructing velocity on a background grid. The method integrates three key components: (1) a vorticity-based particle flow map framework, (2) an accurate Hessian evolution scheme on particles, and (3) a solid boundary treatment for no-through and no-slip conditions in VPFM. These components collectively allow a substantially longer flow map length (3-12 times longer) than the state-of-the-art, enhancing vorticity preservation over extended spatiotemporal domains. We validated the performance of VPFM through diverse simulations, demonstrating its effectiveness in capturing complex vortex dynamics and turbulence phenomena.