A Nitsche-based cut finite element method for a fluid--structure interaction problem

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. T...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Massing, Andre, Larson, Mats G, Logg, Anders, Rognes, Marie E
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 14.04.2015
Subjects:
Computational fluid dynamics
Embedding
Finite element analysis
Finite element method
Fluid-structure interaction
Iterative methods
Iterative solution
Mathematical analysis
Mathematical models
Viscous fluids
ISSN:2331-8422
Online Access:Get full text
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Summary:We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation which allows us to establish stability and optimal order \emph{a priori} error estimates, see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state fluid--structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.1311.2431