Penetration-free Solid-Fluid Interaction on Shells and Rods

TL;DR

The paper tackles robust, penetration-free solid-fluid coupling for thin codimensional solids (shells and rods) by recasting the interaction as a position-level optimization with barrier constraints. It introduces a level-set based distance metric and a unified pipeline that alternates between position prediction, energy-based optimization, and velocity correction to seamlessly couple Eulerian fluids with Lagrangian, codimensional solids while enforcing incompressibility and non-penetration. Key contributions include a barrier-based contact model, a Newton solver with line search filtered by continuous collision detection, and a framework that preserves fluid volume across topology changes and complex interactions, demonstrated on 2D validations and diverse 3D examples. The approach offers a versatile, robust alternative to velocity-based coupling, enabling accurate contact handling and energy-preserving simulations across fluid–shell and fluid–rod scenarios with practical implications for graphics and physics-based simulation.

Abstract

We introduce a novel approach to simulate the interaction between fluids and thin elastic solids without any penetration. Our approach is centered around an optimization system augmented with barriers, which aims to find a configuration that ensures the absence of penetration while enforcing incompressibility for the fluids and minimizing elastic potentials for the solids. Unlike previous methods that primarily focus on velocity coherence at the fluid-solid interfaces, we demonstrate the effectiveness and flexibility of explicitly resolving positional constraints, including both explicit representation of solid positions and the implicit representation of fluid level-set interface. To preserve the volume of the fluid, we propose a simple yet efficient approach that adjusts the associated level-set values. Additionally, we develop a distance metric capable of measuring the separation between an implicitly represented surface and a Lagrangian object of arbitrary codimension. By integrating the inertia, solid elastic potential, damping, barrier potential, and fluid incompressibility within a unified system, we are able to robustly simulate a wide range of processes involving fluid interactions with lower-dimensional objects such as shells and rods. These processes include topology changes, bouncing, splashing, sliding, rolling, floating, and more.

Figures (21)

• Figure 1: Droplets with varying surface tension bounce on a soft cloth. Top: Low surface tension liquid without damping applied to the cloth. Bottom: High surface tension liquid with Rayleigh damping applied to the cloth.
• Figure 2: Dam break intercepted by a non-permeable cloth, illustrating the contrast in fluid motion on each side. The cloth is fixed at the two top corners and five equally spaced vertices at the bottom. The second row showcases intricate surface wrinkles as the cloth interacts with the surrounding liquids.
• Figure 3: A raindrop splashes down, causing deformation of a hydrophobic leaf with high bending stiffness. The raindrop subsequently fractures into multiple smaller droplets of varying scales, which then rebound into the air.
• Figure 4: The level-set unknowns for optimization encompass grid cells within an $\varepsilon$-narrowband surrounding the initial interface. Including regions distant from the interface by more than $\varepsilon$ is unnecessary due to the nearly zero value of the Heaviside function in those areas, resulting in no impact on the fluid volume. The volume integral of the optimized level-set field is expected to precisely match the desired volume $V_0$.
• Figure 5: A primitive pair between the Eulerian fluid and the Lagrangian solid comprises a vertex and the corresponding dual grid cell it occupies. The distance between them is determined by a weighted linear combination of the level-set values at the adjacent primal grid cells, taking into account their relative positions.