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arXiv · 1311.2431

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

Andre Massing·Mats G. Larson·Anders Logg·Marie E. Rognes
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Abstract

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.

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Andre Massing, Mats G. Larson, Anders Logg, Marie E. Rognes. 2013-11-11. A Nitsche-based cut finite element method for a fluid--structure interaction problem. https://doi.org/10.2140/camcos.2015.10.97

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