Fluid Simulation on Vortex Particle Flow Maps

2025-05-28

AI Summary

To address the challenge of long-term simulation of complex vortex structures in incompressible flows with dynamically moving solid boundaries, this paper proposes a novel Vortex-Flowmap framework based on vorticity. It jointly evolves vorticity and flow-map quantities—including the exact Lagrangian advection of the Hessian tensor—on vorticity-based Lagrangian particles, while reconstructing velocity fields on an Eulerian grid. Crucially, it introduces the first tightly coupled projection algorithm that simultaneously enforces differential-geometric evolution of the flow map and no-penetration/no-slip boundary conditions on moving solid walls. The method significantly extends flow-map horizons (by 3–12×) and improves long-time vorticity conservation. It achieves high-fidelity reproduction of intricate vortex dynamics across diverse challenging scenarios, including vortex shedding, turbulence, and strong fluid–structure interactions.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• Simulate incompressible flow with complex vortical evolution
• Handle dynamic solid boundaries in fluid simulation
• Achieve longer flow map distances for vorticity preservation

Innovation

• Vorticity-based particle flow map framework
• Accurate Hessian evolution scheme on particles
• Solid boundary treatment for no-through conditions