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Deriving adequate formulations for fluid-structure interaction problems: From ALE to transpiration. (English) Zbl 1010.74080
Summary: Most formlations describing low-speed large displacement 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 paper is to review the derivation of such formulations, to describe different time discretisation strategies, and to discuss numerical problems which arise when implementing these techniques. To overcome all technical difficulties arising when dealing with moving grids, we 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 here by various numerical experiments.

MSC:
74S20 Finite difference methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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