Fluid Implicit Particles on Coadjoint Orbits (SIGGRAPH Asia 2024) скачать в хорошем качестве

Fluid Implicit Particles on Coadjoint Orbits (SIGGRAPH Asia 2024)

We present a high-order structure-preserving fluid simulation method in the hybrid Eulerian-Lagrangian framework. This discrete Hamiltonian formulation is energy and circulation preserving; formally, the flow evolves on a coadjoint orbit. Publication: Mohammad Sina Nabizadeh, Ritoban Roy-Chowdhury, Hang Yin, Ravi Ramamoorthi and Albert Chern. (2024) Fluid Implicit Particles on Coadjoint Orbits. ACM Transactions on Graphics (TOG), Vol. 43, Issue 6, Article 270. Paper and code are available on the project page: https://cseweb.ucsd.edu/~viscomp/projects/... 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. Music: 'The Long Dark' by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au