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arXiv · 2406.01936

Fluid Implicit Particles on Coadjoint Orbits

Mohammad Sina Nabizadeh·Ritoban Roy-Chowdhury·Hang Yin·Ravi Ramamoorthi·Albert Chern
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Abstract

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.

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Mohammad Sina Nabizadeh, Ritoban Roy-Chowdhury, Hang Yin, Ravi Ramamoorthi, Albert Chern. 2024-06-04. Fluid Implicit Particles on Coadjoint Orbits. https://doi.org/10.1145/3687970

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