Description of a boundary layer phenomenon in acoustic media with a multi-scale expansion. Application

Hélène Barucq 1 Juliette Chabassier 1 Marc Duruflé 1 Victor Péron 1
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : We consider a transmission problem for the propagation of an acoustic wave in heterogeneous media in time-harmonic regime. The domain of interest represents the sun and its atmosphere. This problem involves a large parameter $\alpha$ which corresponds to the exponential decay rate of the density inside the atmosphere. In this framework a boundary layer phenomenon occurs inside the atmosphere. There are several similarities with the skin effect in electromagnetism. We describe the boundary layer phenomenon with a multi-scale expansion in power series of $\alpha −1$. As an application we derive approximate boundary conditions. This approach leads to solve only equations set inside the sun. Numerical results illustrate the accuracy of the approximate models.
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Submitted on : Thursday, January 25, 2018 - 11:33:10 AM
Last modification on : Monday, January 13, 2020 - 2:38:06 PM

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Hélène Barucq, Juliette Chabassier, Marc Duruflé, Victor Péron. Description of a boundary layer phenomenon in acoustic media with a multi-scale expansion. Application. V-MAD 2016 - 6th Valparaíso’s Mathematics and its Applications Days, Jan 2016, Valparaiso, Chile. pp.1-42. ⟨hal-01691684⟩

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