NDLI: Stability and Convergence Analysis of the Extensions of the Kinematically Coupled Scheme for the Fluid-Structure Interaction

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bukac, Martina Muha, Boris
Copyright Year	2016
Abstract	In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, and its extensions for the interaction between an incompressible, viscous fluid and a thin, elastic structure. We consider a benchmark problem where the structure is modeled using a general thin structure model, and the coupling between the fluid and structure is linear. We derive the energy estimates associated with the unconditional stability of an extension of the kinematically coupled scheme, called the $\beta$-scheme. Furthermore, for the first time we present a priori estimates showing optimal, first-order in time convergence in the case where $\beta=1$. We further discuss the extensions of our results to other fluid-structure interaction problems, in particular the fluid-thick structure interaction problem. The theoretical stability and convergence results are supported with numerical examples.
Sponsorship	Croatian Science Foundation. Division of Mathematical Sciences
Starting Page	3032
Ending Page	3061
Page Count	30
File Format	PDF
ISSN	00361429
DOI	10.1137/16M1055396
e-ISSN	10957170
Issue Number	5
Volume Number	54
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-10-04
Access Restriction	Subscribed
Subject Keyword	fluid-structure interaction Fluid-solid interactions Error bounds convergence rates Numerical approximation of solutions Finite element methods Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods error estimates noniterative scheme
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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