An Eulerian Vortex Method on Flow Maps

Abstract

We present an Eulerian vortex method based on the theory of flow maps to simulate the complex vortical motions of incompressible fluids. Central to our method is the novel incorporation of the flow-map transport equations for line elements, which, in combination with a bi-directional marching scheme for flow maps, enables the high-fidelity Eulerian advection of vorticity variables. The fundamental motivation is that, compared to impulse $\mathbf{m}$, which has been recently bridged with flow maps to encouraging results, vorticity $\mathbf{\omega }$ promises to be preferable for its numerical stability and physical interpretability. To realize the full potential of this novel formulation, we develop a new Poisson solving scheme for vorticity-to-velocity reconstruction that is both efficient and able to accurately handle the coupling near solid boundaries. We demonstrate the efficacy of our approach with a range of vortex simulation examples, including leapfrog vortices, vortex collisions, cavity flow, and the formation of complex vortical structures due to solid-fluid interactions.

Accepted at ACM Transactions on Graphics (SIGGRAPH Asia 2024)

References in corpus (7)

• Discrete Exterior Calculus
• Fluid Simulation on Neural Flow Maps
• GroomCap: High-Fidelity Prior-Free Hair Capture
• A Characteristic Mapping Method for the two-dimensional incompressible Euler equations
• A Characteristic Mapping Method for the three-dimensional incompressible Euler equations
• Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps
• Hidden Degrees of Freedom in Implicit Vortex Filaments

Cited by in corpus (1)

• Fluid Simulation on Vortex Particle Flow Maps