Fluid-structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid-structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid-structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

中文翻译：

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浸入式流固耦合方法

流固相互作用在自然界中普遍存在，并且发生在所有生物尺度上。浸入式方法为流体结构系统建模提供了数学和计算框架。这些方法通常使用流体的欧拉描述和结构的拉格朗日描述，可以处理薄的浸没边界和体积体，并且可以对柔性或刚性或以规定的变形运动学移动的结构进行建模。浸入式公式不需要贴体离散化，从而避免了涉及大变形和位移的模型所需的频繁网格再生。本文回顾了弹性结构和具有规定运动学的结构的浸入方法。它考虑使用积分算子连接欧拉和拉格朗日框架的公式以及直接沿流体结构界面应用跳跃条件的方法。基准问题证明了这些方法的有效性，并且选定的雷诺数高达约 20,000 的应用突出了它们在生物和生物医学建模和模拟中的影响。