Immersed Methods for Coupled Continua

10.1142/10833 ◽  
2021 ◽  
Author(s):  
Sheldon Wang ◽  
Lucy Zhang
Keyword(s):  
Immersed Methods

Immersed Methods for High Reynolds Number Fluid-Structure Interactions

2017 ◽  
Vol 14 (06) ◽  
pp. 1750068 ◽  
Author(s):  
Lucy T. Zhang
Keyword(s):  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
High Reynolds Number ◽  
Fluid Structure Interactions ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
High Reynolds ◽  
Immersed Methods ◽  
Reynolds Number Flows

Immersed methods are considered as a class of nonboundary-fitted meshing technique for simulating fluid–structure interactions. However, the conventional approach of coupling the fluid and solid domains, as in the immersed boundary method and the immersed finite element method, often cannot handle high Reynolds number flows interacting with moving and deformable solids. As the solid dynamics is imposed by the fluid dynamics, it often leads to unrealistically large deformation of the solid in cases of high Reynolds number flows. The first attempt in resolving this issue was proposed in the modified immersed finite element method (mIFEM), however, some terms were determined heuristically. In this paper, we provide a full and rigorous derivation for the mIFEM with corrections to the previously proposed terms, which further extends the accuracy of the algorithm. In the “swapped” coupling logic, we solve for the dynamics of the solid, and then numerically impose it to the background fluid, which allows the solid to control its own dynamics and governing laws instead of following that of the fluid. A few examples including a biomedical engineering application are shown to demonstrate the capability in handling large Reynolds number flows using the derived mIFEM.

Combination of Compressible and Incompressible Flow Codes Via Immersed Methods

2008 ◽  
Author(s):  
Rainhald Lohner ◽  
Philippe Ravier ◽  
Pierre de Kermel ◽  
Jean Roger
Keyword(s):  
Incompressible Flow ◽  
Immersed Methods

scholarly journals Immersed Methods for Fluid–Structure Interaction

2020 ◽  
Vol 52 (1) ◽  
pp. 421-448 ◽  
Author(s):  
Boyce E. Griffith ◽  
Neelesh A. Patankar
Keyword(s):  
Fluid Structure Interaction ◽  
Reynolds Numbers ◽  
Benchmark Problems ◽  
Lagrangian Description ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Eulerian Description ◽  
Biomedical Modeling ◽  
Immersed Methods ◽  
Model Structures

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.

Effects of Material Moduli on Compressible Fluid-Solid Systems Using Implicit Immersed Continuum Methods

2008 ◽  
Author(s):  
X. Sheldon Wang
Keyword(s):  
Finite Element ◽  
Compressible Fluid ◽  
Mixed Finite Element ◽  
Test System ◽  
Soft Material ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Volume Conservation ◽  
Conservation Problem ◽  
Immersed Methods

Using a compressible fluid-solid test system, we would like to illustrate the need for implicit immersed continuum method. The implicit mixed finite element formulation for both solid and fluid domains solves the volume conservation problem associated with immersed methods. The immediate extension of the implicit compressible immersed continuum method is to handle continuum-continuum coupling in soft material designs.

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