We propose a novel Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation naturally embodies a perfect flow map. Centered on this concept, we have developed an Eulerian-Lagrangian framework comprising four essential components: Lagrangian particles for a natural and precise representation of bidirectional flow maps; a dual-scale map representation to accommodate the mapping of various flow quantities; a particle-to-grid interpolation scheme for accurate quantity transfer from particles to grid nodes; and a hybrid impulse-based solver to enforce incompressibility on the grid. The efficacy of PFM has been demonstrated through various simulation scenarios, highlighting the evolution of complex vortical structures and the details of turbulent flows. Notably, compared to NFM, PFM reduces computing time by up to 49 times and memory consumption by up to 41%, while enhancing vorticity preservation as evidenced in various tests like leapfrog, vortex tube, and turbulent flow.

翻译：我们提出了一种新颖的粒子流图（PFM）方法，以实现不可压缩流体模拟中精确的长距离平流。该方法的核心出发点在于：前向模拟中生成的粒子轨迹天然蕴含了一个完美的流图。基于这一概念，我们开发了一个由四个关键组成部分构成的欧拉-拉格朗日框架：用于自然且精确表示双向流图的拉格朗日粒子；适应多种流场量映射的双尺度图表示；实现粒子到网格节点精确量传递的粒子-网格插值方案；以及基于混合脉冲的求解器，用于在网格上强制实施不可压缩性。通过多种模拟场景（例如复杂涡旋结构的演化及湍流细节）验证了PFM的有效性。值得注意的是，与NFM相比，PFM在计算时间上最高可减少49倍，内存消耗最高可降低41%，同时在跳跃流、涡管及湍流等测试中表现出更优的涡量保持能力。