Fluid Implicit Particles on Coadjoint Orbits

TL;DR

The paper introduces CO-FLIP, a structure-preserving fluid simulation method that maintains energy and circulation, demonstrating high stability and accuracy even at low resolutions.

Contribution

It develops a novel high-order, structure-preserving fluid simulation approach based on coadjoint orbits and Hamiltonian formulation, improving stability and physical fidelity.

Findings

Energy and circulation are preserved during simulations.

The method achieves stable turbulence effects at low resolutions.

Pressure projection and particle-grid transfers are exact in the weak sense.

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.