Generalized Robin–Neumann explicit coupling schemes for incompressible fluid‐structure interaction: Stability analysis and numerics. (21st October 2014)

• Record Type: Journal Article
• Authors: Fernández, Miguel A.; Mullaert, Jimmy; Vidrascu, Marina
• Is Part Of: International journal for numerical methods in engineering. Volume 101:Number 3(2015)
• Page Start: 199
• Page End: 229
• Publication Date: 2014-10-21
• Subjects: Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4785
• Languages: English
• ISSNs: 0029-5981

Abstract

<abstract abstract-type="main" id="nme4785-abs-0001"> <title>SUMMARY</title> <p id="nme4785-para-0001">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 [<italic>Comput. Methods Appl. Mech. Engrg., 267:566–593, 2013</italic>, <italic>Numer. Math., 123(1):21–65, 2013</italic>] 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 &amp; Sons, Ltd.</p> </abstract>