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.

翻译：我们提出了一种新颖方法，用于模拟流体与薄弹性固体之间无穿透的交互过程。该方法围绕一个附加屏障函数的优化系统展开，旨在求解既能确保无穿透状态，又能满足流体不可压缩性并最小化固体弹性能量的构型。与以往主要关注固液界面速度连续性的方法不同，我们展示了显式解析位置约束（包括固体的显式位置表示与流体的隐式水平集界面表示）的有效性与灵活性。为保持流体体积，我们提出一种简单高效的方案来调整关联的水平集数值。此外，我们发展了一种距离度量方法，能够测量隐式表示曲面与任意余维数拉格朗日物体之间的间隔。通过将惯性、固体弹性能量、阻尼、屏障势能及流体不可压缩性整合于统一系统中，我们能够鲁棒地模拟涉及流体与壳体、杆件等低维物体交互的广泛过程，包括拓扑变化、弹跳、溅射、滑动、滚动、漂浮等。