Linear stability analysis in fluid-structure interaction with transpiration. Part I: formulation and mathematical analysis

Abstract : The aim of this work is to provide a new Linearization Principle approach particularly suited for problems in fluid-structure stability. The complexity here, and the main difference with respect to the classical approach, comes from the fact that the full non-linear fluid equations are written in a moving (i.e. time dependent) domain. The underlying idea of our approach comes from the linearization-transpiration method developed in [11,12]. This allows us to obtain a new coupled spectral problem involving the linearized Navier-Stokes equations and those of a reduced linear structure. The coupling is realized through specific transpiration conditions on a fixed interface, while keeping a fixed fluid domain. Finally, we provide a first rigorous mathematical treatment of this eigenproblem.
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Submitted on : Tuesday, May 23, 2006 - 7:34:41 PM
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Miguel Angel Fernández, Patrick Le Tallec. Linear stability analysis in fluid-structure interaction with transpiration. Part I: formulation and mathematical analysis. [Research Report] RR-4570, INRIA. 2002. ⟨inria-00072018⟩

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