Fluid-structure interaction: analysis of a 3-D compressible model

Abstract

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The Interaction between Quasilinear Elastodynamics and the Navier-Stokes Equations

“…Later, the elastic body was modeled with the restriction of either a finite number of modes ( [8]) or with a hyperviscous type law for the solid ( [2], [10]), essentially by the same type of Eulerian global variational methods developed in [7]. For the steady-state problem, which is elliptic in both phases, [11] solved the case of solid modeled as a St. Venant-Kirchhoff material.…”

Existence of weak solutions for an interaction problem between an elastic structure and a compressible viscous fluid

“…The method presented in [5] has already been adapted in the case of a rigid structure immersed in a compressible fluid in [4]. For other studies dealing with interaction between a compressible fluid and a structure we refer also to [6] for an elastic structure and [2] for a rigid structure.…”

Existence for a Three-Dimensional Steady State Fluid-Structure Interaction Problem

“…The equations (11,12,13) completed with the structure constitutive equation (5) enable us to associate to a given displacement b another displacement u(b). We denote by S this mapping.…”

“…So, we just built a mapping S that associates to each b ∈ X p , a displacement u(b) ∈ W 2,p (Ω s ), which is the unique solution of (12). The existence of a solution for the coupled problem follows from the existence of at least one fixed point of the mapping S. So, next, in order to prove the S has at least one fixed point, we check that the hypotheses of Schauder-Tychonov's fixed point theorem (see [10], pp.…”

“…For an existence result on a plate interacting with a linear Vol. 4 (2002) Existence for Fluid-Structure Interaction Problem 77 compressible flow, we refer to [11], [12].…”