Vol. 10, No. 2, 2015

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A Nitsche-based cut finite element method for a fluid-structure interaction problem

André Massing, Mats G. Larson, Anders Logg and Marie E. Rognes

Vol. 10 (2015), No. 2, 97–120
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 that 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 that allows us to establish stability and optimal-order a priori error estimates. 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.

Keywords
fluid-structure interaction, overlapping meshes, cut finite element method, embedded meshes, stabilized finite element methods, Nitsche's method
Mathematical Subject Classification 2010
Primary: 65N12, 65N30, 74B20, 76D07, 65N85
Milestones
Received: 11 November 2013
Revised: 21 February 2015
Accepted: 3 April 2015
Published: 4 September 2015
Authors
André Massing
Department of Mathematics and Mathematical Statistics
Umeå University
901 87 Umeå
Sweden
Mats G. Larson
Department of Mathematics and Mathematical Statistics
Umeå University
901 87 Umeå
Sweden
Anders Logg
Department of Mathematical Sciences
Chalmers University of Technology
412 96 Göteborg
Sweden
Department of Mathematical Sciences
University of Gothenburg
412 61 Göteborg
Sweden
Marie E. Rognes
Simula Research Laboratory
1364 Fornebu
Norway