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Partitioned iterative solution methods for fluid–structure interaction
Author(s) -
van Brummelen E. H.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2465
Subject(s) - fluid–structure interaction , convergence (economics) , mathematics , generalized minimal residual method , operator (biology) , compressibility , compressible flow , iterative method , added mass , mathematical analysis , finite element method , computer science , mathematical optimization , physics , mechanics , vibration , transcription factor , economics , economic growth , thermodynamics , biochemistry , chemistry , repressor , quantum mechanics , gene
The basic subiteration method for fluid–structure interaction (FSI) problems is based on a partitioning of the fluid–structure system into a fluidic part and a structural part. The effect of the fluid on the structure can be represented by an added mass to the structural operator. This added mass can be identified as an upper bound on the norm or spectral radius of the Poincar'e–Steklov operator of the fluid. The convergence behavior of the subiteration method depends sensitively on the ratio of the added mass to the actual structural mass. For FSI problems with large added‐mass effects, the subiteration method is either unstable or its convergence behavior is prohibitively inefficient. In recent years, several more advanced partitioned iterative solution methods have been proposed for this class of problems, which use subiteration as a component. The rudimentary characterization of the Poincaré–Steklov operator provided by the added mass is, however, inadequate to analyze these methods. Moreover, this characterization is inappropriate for compressible flows. In this paper, we investigate the fine properties of the Poincaré–Steklov operators and of the corresponding subiteration operators for incompressible‐ and compressible flow models and for two distinct structural operators. Based on the characteristic properties of the subiteration operators, we subsequently examine the convergence behavior of several partitioned iterative solution methods for FSI, viz. subiteration, subiteration in conjunction with underrelaxation, the modified‐mass method, Aitken's method, and interface‐GMRES and interface‐Newton–Krylov methods. Copyright © 2010 John Wiley & Sons, Ltd.