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Linear stability analysis in fluid-structure interaction with transpiration. Part II: Numerical analysis and applications

Miguel Angel Fernández 1 Patrick Le Tallec 2
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : This paper constitutes the numerical counterpart of the mathematical framework introduced in Part I. We address the problem of flutter analysis of a coupled fluid-structure system involving an incompressible Newtonian fluid and a reduced structure. We use the Linearization Principle approach developed in Part I, particularly suited for fluid-structure problems involving moving boundaries. Thus, the stability analysis is reduced to the computation of the leftmost eigenvalues of a coupled eigenproblem of minimal complexity. This eigenproblem involves the linearized incompressible Navier-Stokes equations and those of a reduced linear structure. The coupling is realized through specific transpiration interface conditions. The eigenproblem is discretized using a finite element approximation and its smallest real part eigenvalues are computed by combining a generalized Cayley transform and an implicit restarted Arnoldi method. Finally, we report three numerical experiments : a structure immersed in a fluid at rest, a cantilever pipe conveying a fluid flow and a rectangular bridge deck profile under wind effects. The numerical results are compared to former approaches and experimental data. The quality of these numerical results is very satisfactory and promising.
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https://hal.inria.fr/hal-00705123
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Submitted on : Wednesday, June 6, 2012 - 7:45:49 PM
Last modification on : Thursday, September 24, 2020 - 4:00:21 PM

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Miguel Angel Fernández, Patrick Le Tallec. Linear stability analysis in fluid-structure interaction with transpiration. Part II: Numerical analysis and applications. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2003, 192 (43), pp.4837-4873. ⟨10.1016/j.cma.2003.08.001⟩. ⟨hal-00705123⟩

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