AI 中文总结
研究流体与复杂边界相互作用模拟难题，提出FastVEM框架，采用虚拟单元法离散、特定网格构建策略及加速压力投影的求解器，相比先前方法，大幅加速压力投影阶段，能处理更复杂边界几何。
AI 中文摘要
流体与边界相互作用产生的复杂运动虽视觉效果引人入胜，但在复杂边界存在时模拟困难且计算成本高。精确解析边界几何需通过切割单元法构建贴体网格，这常导致压力投影阶段线性系统条件不佳及高昂计算成本。我们提出FastVEM，一个高效的边界贴合流体模拟框架，能以大幅降低的成本实现高保真流 - 边界相互作用。通过数值离散、网格构建和线性求解器的协同自上而下设计实现计算效率。采用虚拟单元法离散以在不规则贴体网格上稳健执行不可压缩性和边界条件，用VEM多项式空间粒子网格法进行平流。引入保持凸性的切割单元策略构建利于模拟的贴体网格。为加速压力投影，开发了具有无扩散延拓算子防止粗级别矩阵致密化的Galerkin几何多重网格求解器，以及确保粗级别自由度合理放置的嵌套边界感知网格层次结构。与基于切割单元的先前流体模拟器相比，FastVEM将计算主导的压力投影阶段加速达100倍，同时能稳健处理更具挑战性的边界几何。
英文摘要
The intricate motion arising from fluid--boundary interactions is visually compelling, yet notoriously difficult and computationally expensive to simulate in the presence of complex boundaries. Accurately resolving boundary geometry requires body-fitted grids constructed via cut-cell methods, which often leads to poorly conditioned linear systems in the pressure projection stage and, consequently, prohibitive computational cost. We present FastVEM, an efficient boundary-conforming fluid simulation framework that enables high-fidelity flow--boundary interaction at substantially reduced cost. Computational efficiency is achieved through a coordinated, top-down design spanning numerical discretization, grid construction, and linear solvers. FastVEM adopts a Virtual Element Method (VEM) discretization to robustly enforce incompressibility and boundary conditions on irregular body-fitted grids, and employs a VEM polynomial-space Particle-in-Cell scheme for advection. Complementing this discretization, a convexity-preserving cut-cell strategy is introduced to construct simulation-friendly body-fitted grids. To accelerate pressure projection, we develop a Galerkin geometric multigrid solver featuring a diffusion-free prolongation operator that prevents coarse-level matrix densification, along with a nested, boundary-aware grid hierarchy that ensures well-posed placement of coarse-level degrees of freedom. Compared to prior cut-cell--based fluid simulators, FastVEM speeds up the computationally dominant pressure projection stage by up to 100x, while robustly handling even more challenging boundary geometries.
Journal refACM Transactions on Graphics, Vol. 45, No. 4, Article 65, 18 pages, July 2026
DOI：10.1145/3811315
