Fluid Simulation on Vortex Particle Flow Maps
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912399487926272 |
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| author | Wang, Sinan Zhou, Junwei Feng, Fan Li, Zhiqi Sun, Yuchen Chen, Duowen Turk, Greg Zhu, Bo |
| author_facet | Wang, Sinan Zhou, Junwei Feng, Fan Li, Zhiqi Sun, Yuchen Chen, Duowen Turk, Greg Zhu, Bo |
| contents | We propose the Vortex Particle Flow Map (VPFM) method to simulate incompressible flow with complex vortical evolution in the presence of dynamic solid boundaries. The core insight of our approach is that vorticity is an ideal quantity for evolution on particle flow maps, enabling significantly longer flow map distances compared to other fluid quantities like velocity or impulse. To achieve this goal, we developed a hybrid Eulerian-Lagrangian representation that evolves vorticity and flow map quantities on vortex particles, while reconstructing velocity on a background grid. The method integrates three key components: (1) a vorticity-based particle flow map framework, (2) an accurate Hessian evolution scheme on particles, and (3) a solid boundary treatment for no-through and no-slip conditions in VPFM. These components collectively allow a substantially longer flow map length (3-12 times longer) than the state-of-the-art, enhancing vorticity preservation over extended spatiotemporal domains. We validated the performance of VPFM through diverse simulations, demonstrating its effectiveness in capturing complex vortex dynamics and turbulence phenomena. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_21946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fluid Simulation on Vortex Particle Flow Maps Wang, Sinan Zhou, Junwei Feng, Fan Li, Zhiqi Sun, Yuchen Chen, Duowen Turk, Greg Zhu, Bo Graphics Fluid Dynamics We propose the Vortex Particle Flow Map (VPFM) method to simulate incompressible flow with complex vortical evolution in the presence of dynamic solid boundaries. The core insight of our approach is that vorticity is an ideal quantity for evolution on particle flow maps, enabling significantly longer flow map distances compared to other fluid quantities like velocity or impulse. To achieve this goal, we developed a hybrid Eulerian-Lagrangian representation that evolves vorticity and flow map quantities on vortex particles, while reconstructing velocity on a background grid. The method integrates three key components: (1) a vorticity-based particle flow map framework, (2) an accurate Hessian evolution scheme on particles, and (3) a solid boundary treatment for no-through and no-slip conditions in VPFM. These components collectively allow a substantially longer flow map length (3-12 times longer) than the state-of-the-art, enhancing vorticity preservation over extended spatiotemporal domains. We validated the performance of VPFM through diverse simulations, demonstrating its effectiveness in capturing complex vortex dynamics and turbulence phenomena. |
| title | Fluid Simulation on Vortex Particle Flow Maps |
| topic | Graphics Fluid Dynamics |
| url | https://arxiv.org/abs/2505.21946 |