Fluid Implicit Particles on Coadjoint Orbits
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912035929849856 |
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| author | Nabizadeh, Mohammad Sina Roy-Chowdhury, Ritoban Yin, Hang Ramamoorthi, Ravi Chern, Albert |
| author_facet | Nabizadeh, Mohammad Sina Roy-Chowdhury, Ritoban Yin, Hang Ramamoorthi, Ravi Chern, Albert |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01936 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fluid Implicit Particles on Coadjoint Orbits Nabizadeh, Mohammad Sina Roy-Chowdhury, Ritoban Yin, Hang Ramamoorthi, Ravi Chern, Albert Graphics Fluid Dynamics 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. |
| title | Fluid Implicit Particles on Coadjoint Orbits |
| topic | Graphics Fluid Dynamics |
| url | https://arxiv.org/abs/2406.01936 |