发表机构
Stockholm University; KTH Royal Institute of Technology（斯德哥尔摩大学; 瑞典皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出含液滴斯托克斯流的代理建模策略，基于多保真框架，用最低保真时液滴作被动示踪剂，导出误差方程修正流场，交替用两种保真度模型，还开发离线 - 在线策略，数值实验验证其准确性和效率。
AI 中文摘要
我们提出了一种用于在载液中悬浮有液滴的斯托克斯流的代理建模策略。我们的方法基于多保真框架。在最低保真度下，液滴被视为被动示踪剂，忽略它们对周围流场的影响。基于此近似，我们推导了一个表示当前建模误差的偏微分方程。然后近似求解该误差方程以校正流场，并迭代该过程。以交替方式使用两种保真度：无液滴时的斯托克斯流和自由空间中单个液滴周围的流。通过系统地组合这些模型，该方法捕获液滴 - 流、液滴 - 边界和液滴 - 液滴相互作用。对于几何相似的液滴，我们进一步开发了一种有效的离线 - 在线策略，通过重用预先计算的单液滴解来利用这种结构。数值实验在各种测试中证明了所提出代理的准确性和效率，包括多达10000个液滴的场景。值得注意的是，我们表明与使用最先进软件的完全解析多流体模拟相比，所提出的代理实现了显著降低的计算成本。
英文摘要
We present a surrogate modeling strategy for Stokes flows with liquid droplets suspended in a carrier fluid. Our approach is based on a multi-fidelity framework. At the lowest fidelity, droplets are treated as passive tracers, neglecting their influence on the ambient flow field. Building on this approximation, we derive a PDE that represents the current modeling error. This error equation is then solved approximately to correct the flow field and the procedure is iterated. Two fidelities are employed in an alternating fashion: Stokes flow in the absence of droplets and flow around a single droplet in free space. By systematically combining these models, the method captures droplet-flow, droplet-boundary, and droplet-droplet interactions. In this work, the framework is developed and validated for circular, non-deforming droplets in two spatial dimensions. The geometric self-similarity of the droplets allows us to construct an efficient offline-online strategy based on the reuse of precomputed single-droplet solutions. Extensions to deformable droplets are also discussed. Numerical experiments demonstrate the accuracy and efficiency of the proposed surrogate in a variety of tests, including scenarios with up to $10^4$ droplets. Notably, we show that the proposed surrogate achieves substantially reduced computational cost compared to fully resolved multi-fluid simulations with state-of-the-art software.
