Solid-Fluid Interaction on Particle Flow Maps

TL;DR

The paper tackles solid-fluid interaction within a flow-map framework by representing both fluid and solid as particle-based flow maps of differing lengths. It introduces two main mechanisms—impulse-to-velocity transfer and particle path-integral accumulation—to enable momentum exchange and force integration across the map trajectories, enabling coupling with classical models like MPM and IBM. The approach preserves vortical structures, demonstrates stability and accuracy across 2D/3D vortex-rich scenarios, and provides a versatile pipeline adaptable to existing solid-fluid coupling paradigms. The work offers a path toward integrating traditional coupling strategies into flow-map methods, with potential impact on visually rich, physically accurate vortex-solid interactions in graphics and physics simulations.

Abstract

We propose a novel solid-fluid interaction method for coupling elastic solids with impulse flow maps. Our key idea is to unify the representation of fluid and solid components as particle flow maps with different lengths and dynamics. The solid-fluid coupling is enabled by implementing two novel mechanisms: first, we developed an impulse-to-velocity transfer mechanism to unify the exchanged physical quantities; second, we devised a particle path integral mechanism to accumulate coupling forces along each flow-map trajectory. Our framework integrates these two mechanisms into an Eulerian-Lagrangian impulse fluid simulator to accommodate traditional coupling models, exemplified by the Material Point Method (MPM) and Immersed Boundary Method (IBM), within a particle flow map framework. We demonstrate our method's efficacy by simulating solid-fluid interactions exhibiting strong vortical dynamics, including various vortex shedding and interaction examples across swimming, falling, breezing, and combustion.

Figures (25)

• Figure 1: Particle Flow Map starting from time $a$ and ending at time $c$.
• Figure 2: Illustration for mapping coupling force from current to initial frame.
• Figure 3: Illustration of the key idea of our method where we convert impulse to velocity using our particle buffers $\bm \Lambda$ and $\bm \Upsilon$. The problem of direct coupling between impulse and velocity is shown in Section \ref{['sec:ablation']}. Our whole pipeline is shown in Section 5 and the adaptation of our method to classical coupling methods is shown in Section \ref{['sec:ibm']} and \ref{['sec:mpm']}.
• Figure 4: We show the path and vorticity snapshots of free falling leaf and parachute. The falling path of the leaf is shown on the left. We can clearly observe the falling path experienced three stages: acceleration, converging, and chaos which accords with real-life observation. On the right, we show a parachute falling and we observe velocity convergence after the acceleration stage as expected.
• Figure 5: Under incoming flow with variant velocity, turbulent surface flow is created from the grass geometry. Vorticity is being visualized here for illustration of the turbulent flow.