Deriving adequate formulations for fluid-structure interaction problems: From ALE to transpiration

Most formulations describing low speed large displacements fluid-structure interaction problems use a totally lagrangian formulation for the structure, and an Arbitrary Euler Lagrange (ALE) formulation for the fluid. The purpose of the presellt 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 illterface boundary conditions. This last formulation is rather popular in the aeronautical community, and will be illustrated by various numerical experiments.