Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps
arxiv(2024)
摘要
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
evidenced in various tests like leapfrog, vortex tube, and turbulent flow.
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