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Graph."],"published-print":{"date-parts":[[2024,12,19]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1145\/3687970","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T15:46:04Z","timestamp":1732031164000},"page":"1-38","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Fluid Implicit Particles on Coadjoint Orbits"],"prefix":"10.1145","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2182-5197","authenticated-orcid":false,"given":"Mohammad Sina","family":"Nabizadeh","sequence":"first","affiliation":[{"name":"University of California San Diego, La Jolla, United States of America"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7823-9260","authenticated-orcid":false,"given":"Ritoban","family":"Roy-Chowdhury","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, United States of America"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1994-331X","authenticated-orcid":false,"given":"Hang","family":"Yin","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, United States of America"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3993-5789","authenticated-orcid":false,"given":"Ravi","family":"Ramamoorthi","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, United States of America"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9802-3619","authenticated-orcid":false,"given":"Albert","family":"Chern","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, United States of America"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2024,11,19]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the ACM in Computer Graphics and Interactive Techniques 2, 2, Article 14 (July","author":"Aanjaneya Mridul","year":"2019","unstructured":"Mridul Aanjaneya, Chengguizi Han, Ryan Goldade, and Christopher Batty. 2019. 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