We propose Coadjoint Orbit FLIP (CO-FLIP), a high order accurate, structure preserving fluid simulation method in the hybrid Eulerian-Lagrangian framework. We start with a Hamiltonian formulation of the incompressible Euler Equations, and then, using a local, explicit, and high order divergence free interpolation, construct a modified Hamiltonian system that governs our discrete Euler flow. The resulting discretization, when paired with a geometric time integration scheme, is energy and circulation preserving (formally the flow evolves on a coadjoint orbit) and is similar to the Fluid Implicit Particle (FLIP) method. CO-FLIP enjoys multiple additional properties including that the pressure projection is exact in the weak sense, and the particle-to-grid transfer is an exact inverse of the grid-to-particle interpolation. The method is demonstrated numerically with outstanding stability, energy, and Casimir preservation. We show that the method produces benchmarks and turbulent visual effects even at low grid resolutions.

中文翻译：

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共伴轨道上的流体隐式粒子


我们提出了 Coadjoint Orbit FLIP （CO-FLIP），这是一种在混合 Eulerian-Lagrangian 框架中的高阶精确、结构保持流体模拟方法。我们从不可压缩欧拉方程的哈密顿公式开始，然后使用局部、显式和高阶无散度插值，构造一个改进的哈密顿系统来控制我们的离散欧拉流。当与几何时间积分方案配对时，产生的离散化是能量和循环守恒的（正式流动在共伴轨道上演化），类似于流体隐含粒子 （FLIP） 方法。CO-FLIP 具有多个附加属性，包括压力投影在弱意义上是精确的，并且粒子到网格的传输是网格到粒子插值的精确倒数。该方法以数字方式证明了出色的稳定性、能量和卡西米尔守恒。我们表明，即使在低网格分辨率下，该方法也能产生基准和湍流视觉效果。