Curl-Flow：用于基于网格流体的边界保持逐点不可压缩速度插值
Curl-Flow: Boundary-Respecting Pointwise Incompressible Velocity Interpolation for Grid-Based Fluids
AI总结：
本文提出Curl-Flow框架，通过快速并行扫描和规范变换恢复离散向量势，实现逐点无散度速度插值，在较低额外成本下显著改善了粒子轨迹与不可压缩性。
摘要：
我们提出用逐点无散度速度插值来增强标准的基于网格的流体求解器，从而确保在子单元级别上实现精确的不可压缩性。我们的方法以由交错网格压力投影生成的离散无散度速度场作为输入，并首先恢复相应的离散向量势。我们没有为该势函数求解代价高昂的向量泊松问题，而是开发了一种快速并行扫描策略来寻找候选势函数，并应用规范变换来强制执行库仑规范条件，从而使其在数值上变得平滑。对该离散势函数进行插值会生成一个逐点向量势，其解析旋度即为一个逐点不可压缩的速度场。我们的方法进一步通过使用基于水平集的切割单元以及一种受 Curl-Noise 启发的新型势函数爬升程序来支持不规则固体几何形状，该程序同时提供严格无穿透速度和不可压缩性。实验比较表明，作为我们方法核心的向量势重建过程始终快于先前的此类重建方案，尤其是那些求解向量泊松问题的方案。此外，作为其适度额外成本的回报，我们的整体 Curl-Flow 框架产生了显著改善的粒子轨迹，这些轨迹严格尊重不规则障碍物，不会受到虚假源或汇的影响，并随时间推移产生更优的粒子分布。
英文摘要：
We propose to augment standard grid-based fluid solvers with pointwise divergence-free velocity interpolation, thereby ensuring exact incompressibility down to the sub-cell level. Our method takes as input a discretely divergence-free velocity field generated by a staggered grid pressure projection, and first recovers a corresponding discrete vector potential. Instead of solving a costly vector Poisson problem for the potential, we develop a fast parallel sweeping strategy to find a candidate potential and apply a gauge transformation to enforce the Coulomb gauge condition and thereby make it numerically smooth. Interpolating this discrete potential generates a pointwise vector potential whose analytical curl is a pointwise incompressible velocity field. Our method further supports irregular solid geometry through the use of level set-based cut-cells and a novel Curl-Noise-inspired potential ramping procedure that simultaneously offers strictly non-penetrating velocities and incompressibility. Experimental comparisons demonstrate that the vector potential reconstruction procedure at the heart of our approach is consistently faster than prior such reconstruction schemes, especially those that solve vector Poisson problems. Moreover, in exchange for its modest extra cost, our overall Curl-Flow framework produces significantly improved particle trajectories that closely respect irregular obstacles, do not suffer from spurious sources or sinks, and yield superior particle distributions over time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
