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The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid.
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Immersed Methods for Fluid–Structure Interaction
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.
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- PAR ID:
- 10176152
- Date Published:
- Journal Name:
- Annual Review of Fluid Mechanics
- Volume:
- 52
- Issue:
- 1
- ISSN:
- 0066-4189
- Page Range / eLocation ID:
- 421 to 448
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1146/annurev-fluid-010719-060228
