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Generalized Robin–Neumann explicit coupling schemes for incompressible fluid‐structure interaction: Stability analysis and numerics
Author(s) -
Fernández Miguel A.,
Mullaert Jimmy,
Vidrascu Marina
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4785
Subject(s) - mathematics , coupling (piping) , convergence (economics) , von neumann architecture , compressibility , stability (learning theory) , numerical analysis , fluid–structure interaction , theory of computation , a priori and a posteriori , mathematical analysis , finite element method , computer science , pure mathematics , physics , mechanics , algorithm , mechanical engineering , philosophy , epistemology , machine learning , engineering , economics , thermodynamics , economic growth
SUMMARY We introduce a new class of explicit coupling schemes for the numerical solution of fluid‐structure interaction problems involving a viscous incompressible fluid and an elastic structure. These methods generalize the arguments reported in [ Comput. Methods Appl. Mech. Engrg., 267:566–593, 2013 , Numer. Math., 123(1):21–65, 2013 ] to the case of the coupling with thick‐walled structures. The basic idea lies in the derivation of an intrinsic interface Robin consistency at the space semi‐discrete level, using a lumped‐mass approximation in the structure. The fluid–solid splitting is then performed through appropriate extrapolations of the solid velocity and stress on the interface. Based on these methods, a new, parameter‐free, Robin–Neumann iterative procedure is also proposed for the partitioned solution of implicit coupling. A priori energy estimates, guaranteeing the stability of the schemes and the convergence of the iterative procedure, are established within a representative linear setting. The accuracy and performance of the methods are illustrated in several numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.