Physics

Geology

Finite element method

Reynolds number

Fluid–structure interaction

Mathematics

Lagrangian

Mechanics

Boundary (topology)

Immersed boundary method

Geodesy

Mathematical analysis

Benchmark (surveying)

Turbulence

Material point method

Grid

Geometry

Computer science

Eulerian path

Jump

Quantum mechanics

Applied mathematics

Kinematics

Classical mechanics

Thermodynamics

Annual Review of Fluid Mechanics

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.

Immersed Methods for Fluid–Structure Interaction