Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps

TL;DR

This paper introduces a Particle Flow Map (PFM) method that improves long-range fluid advection accuracy and efficiency in incompressible fluid simulations by leveraging particle trajectories as flow maps within an Eulerian-Lagrangian framework.

Contribution

The paper presents a novel PFM approach that combines particle trajectories, dual-scale flow representations, and a hybrid solver to enhance simulation accuracy and reduce computational costs.

Findings

Reduces computation time by up to 49 times.

Reduces memory usage by up to 41%.

Improves vorticity preservation in turbulent flows.

Abstract

We propose a novel Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation naturally embodies a perfect flow map. Centered on this concept, we have developed an Eulerian-Lagrangian framework comprising four essential components: Lagrangian particles for a natural and precise representation of bidirectional flow maps; a dual-scale map representation to accommodate the mapping of various flow quantities; a particle-to-grid interpolation scheme for accurate quantity transfer from particles to grid nodes; and a hybrid impulse-based solver to enforce incompressibility on the grid. The efficacy of PFM has been demonstrated through various simulation scenarios, highlighting the evolution of complex vortical structures and the details of turbulent flows. Notably, compared to NFM, PFM reduces computing time by up to 49 times and memory consumption by up to 41%, while enhancing vorticity preservation as evidenced in various tests like leapfrog, vortex tube, and turbulent flow.