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A fast method for solving fluid–structure interaction problems numerically
Author(s) -
Murea C. M.,
Sy S.
Publication year - 2008
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.1931
Subject(s) - fluid–structure interaction , mathematics , broyden–fletcher–goldfarb–shanno algorithm , euler equations , position (finance) , euler's formula , linear elasticity , mathematical analysis , mathematical optimization , computer science , finite element method , physics , computer network , asynchronous communication , finance , economics , thermodynamics
Abstract The paper presents a semi‐implicit algorithm for solving an unsteady fluid–structure interaction problem. The algorithm for solving numerically the fluid–structure interaction problems was obtained by combining the backward Euler scheme with a semi‐implicit treatment of the convection term for the Navier–Stokes equations and an implicit centered scheme for the structure equations. The structure is governed either by the linear elasticity or by the non‐linear St Venant–Kirchhoff elasticity models. At each time step, the position of the interface is predicted in an explicit way. Then, an optimization problem must be solved, such that the continuity of the velocity as well as the continuity of the stress hold at the interface. During the Broyden, Fletcher, Goldforb, Shano (BFGS) iterations for solving the optimization problem, the fluid mesh does not move, which reduces the computational effort. The term ‘semi‐implicit’ used for the fully algorithm means that the interface position is computed explicitly, while the displacement of the structure, velocity and the pressure of the fluid are computed implicitly. Numerical results are presented. Copyright © 2008 John Wiley & Sons, Ltd.