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.