Equivalent boundary conditions for acoustic media with exponential densities. Application to the atmosphere in helioseismology

Abstract : We present equivalent boundary conditions and asymptotic models for the solution of a transmission problem set in a domain which represents the Sun and its atmosphere. This problem models the propagation of an acoustic wave in time-harmonic regime. The specific non-standard feature of this problem lies in the presence of a small parameter $\delta$ which represents the inverse rate of the exponential decay of the density in the atmosphere. The atmosphere can be approximated by local equivalent boundary conditions for small values of this parameter. We derive rigorously equivalent conditions up to the fourth order of approximation with respect to $\delta$ for the exact solution u. The construction of equivalent conditions is based on a multiscale expansion in power series of $\delta$ for u. Numerical results illustrate the good behavior of these equivalent boundary conditions for realistic values close to those observed for the Sun. Finally we measure the boundary layer phenomenon by introducing a "skin depth" function that turns out to depend on the mean curvature of the interface between the subdomains.
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Juliette Chabassier, Marc Durufle, Victor Péron. Equivalent boundary conditions for acoustic media with exponential densities. Application to the atmosphere in helioseismology. [Research Report] RR-8954, Inria Bordeaux Sud-Ouest; Université de Pau et des Pays de l'Adour; Université de Bordeaux. 2016. ⟨hal-01371580⟩

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