Griffith Boyce E, Patankar Neelesh A
Departments of Mathematics, Applied Physical Sciences, and Biomedical Engineering, University of North Carolina, Chapel Hill, North Carolina 27599, USA.
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Annu Rev Fluid Mech. 2020;52:421-448. doi: 10.1146/annurev-fluid-010719-060228. Epub 2019 Sep 5.
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.
流固相互作用在自然界中无处不在，且发生在所有生物尺度上。浸入式方法为流固系统建模提供了数学和计算框架。这些方法通常采用流体的欧拉描述和结构的拉格朗日描述，可以处理薄浸入边界和体积体，并且能够对柔性或刚性结构或具有规定变形运动学的移动结构进行建模。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可能需要的频繁网格再生。本文回顾了弹性结构和具有规定运动学的结构的浸入式方法。它考虑了使用积分算子连接欧拉框架和拉格朗日框架的公式，以及直接沿流固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，在雷诺数高达约20000的选定应用突出了它们在生物和生物医学建模与模拟中的影响。
