Immersed Methods for Fluid–Structure Interaction

Abstract

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.

Direct numerical simulation of turbulent flow through a ribbed square duct

“…Besides BFM, the immersed boundary method (IBM) can be also considered. The IBM method started with Peskin (1972) and has been significantly developed since (Mittal & Iaccarino 2005; Griffith & Patankar 2020). The IBM method has been successfully applied to DNS and LES of turbulent flows over regular and irregular shaped roughness elements (Leonardi etal.…”

“…Besides BFM, the immersed boundary method (IBM) can be also considered. The IBM method started with Peskin (1972) and has been significantly developed since (Mittal & Iaccarino 2005;Griffith & Patankar 2020). The IBM method has been successfully applied to DNS and LES of turbulent flows over regular and irregular shaped roughness elements (Leonardi et al 2003;Orlandi et al 2006;Scotti 2006;Bhaganagar 2008;Pinelli et al 2010a;Lee, Sung & Krogstad 2011;Yuan & Piomelli 2014;Bhaganagar & Chau 2015;Rouhi, Chung & Hutchins 2019).…”

Fluid–Structure Interaction Models of Bioprosthetic Heart Valve Dynamics in an Experimental Pulse Duplicator

“…One of the earliest of these types of approaches is the immersed boundary (IB) method [12], which was introduced by Peskin to simulate heart valves [13,14]. The IB formulation allows the structural discretization to be independent of the fluid grid and thereby facilitates models with very large structural deformations [15]. Extensions to the IB method have also been used to simulate heart valves [16,17], but in most cases, these prior simulations were not fully resolved, and the valve leaflets were described using only simple structural models based on linear elasticity.…”

Fluid Dynamics of Ballistic Strategies in Nematocyst Firing

“…The fully-coupled fluid-structure interaction model describing the moving barb, the passive, flexible prey and the surrounding fluid is numerically solved by implementing the model in an immersed boundary framework [29,30]. The immersed boundary method has been successfully used to model a variety of biological fluid dynamics problems at intermediate Re (0.01 < Re < 1000) (e.g., [31][32][33]). The elastic structures describing the barb and the prey are defined in a moving Lagrangian framework, while the surrounding fluid is described in a fixed Eulerian framework using the Navier-Stokes equations for a viscous, incompressible fluid,…”