Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer

Victor Péron 1, 2, *
* Corresponding author
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : In this paper we present equivalent conditions and asymptotic models for the diffraction problem of elasto-acoustic waves in a solid medium surrounded by a thin layer of fluid medium. This problem is well suited for the notion of equivalent conditions : since the thickness of the layer is small with respect to the wavelength, the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the third order for the elastic displacement. These conditions approximate the acoustic waves which propagate in the fluid region. This approach leads us to solve only elastic equations. The construction of equivalent conditions is based on a multiscale expansion in power series of the thickness of the layer for the solution of the transmission problem.
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Victor Péron. Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer. [Research Report] RR-8163, INRIA. 2013, pp.32. ⟨hal-00763181v2⟩

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