Deriving Adequate Formulations for Fluid-Structure Interaction Problems: from ALE to Transpiration

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Abstract
Most formulations describing low speed large displacements fluid-structure interaction problems use a totally lagrangian formulation for the structure, and an Arbitrary Eider Lagrange (ALE) formulation for the fluid. The purpose of the present paper is to review the derivation of such formulations, to describe different time discretisation strategies and to explain the type of numerical problems which arise when implementing these techniques. To overcome all technical difficulties arising when dealing with moving grids, we will also explain how an adequate asymptotic expansion can reduce the problem to a standard problem written on a fixed configuration, but using specific transpiration interface boundary conditions. This last formulation is rather popular in the aeronautical community, and will be illustrated by various numerical experiments.