We present a flexible model reduction method for simulating incompressible fluids. We derive a novel vector field basis composed of localized basis flows which have simple analytic forms and can be tiled on regular lattices, avoiding the use of complicated data structures or neighborhood queries. Local basis flow interactions can be precomputed and reused to simulate fluid dynamics on any simulation domain without additional overhead. We introduce heuristic simulation dynamics tailored to our basis and derived from a projection of the Navier‐Stokes equations to produce physically plausible motion, exposing intuitive parameters to control energy distribution across scales. Our basis can adapt to curved simulation boundaries, can be coupled with dynamic obstacles, and offers simple adjustable trade‐offs between speed and visual resolution.

中文翻译：

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模型减少烟雾模拟的本地基础

我们提出了一种用于模拟不可压缩流体的灵活模型简化方法。我们推导出由局部基流组成的新向量场基，这些基流具有简单的解析形式，可以平铺在规则格上，避免使用复杂的数据结构或邻域查询。局部基础流相互作用可以预先计算并重复使用，以在任何模拟域上模拟流体动力学，而无需额外开销。我们引入了根据我们的基础量身定制的启发式模拟动力学，并从 Navier-Stokes 方程的投影导出，以产生物理上合理的运动，暴露直观参数以控制跨尺度的能量分布。我们的基础可以适应弯曲的模拟边界，可以与动态障碍物相结合，并在速度和视觉分辨率之间提供简单的可调权衡。