CHABASSIER, Juliette; DURUFLÉ, Marc; PÉRON, Victor

doi:10.1016/j.amc.2019.04.065

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CHABASSIER, Juliette
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]
Laboratoire de Mathématiques et de leurs Applications [Pau] [LMAP]

DURUFLÉ, Marc
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]
Institut de Mathématiques de Bordeaux [IMB]

PÉRON, Victor
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]
Université de Pau et des Pays de l'Adour [UPPA]
Laboratoire de Mathématiques et de leurs Applications [Pau] [LMAP]

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Applied Mathematics and Computation. 2019-11, vol. 361, p. 177-197

Elsevier

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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 δ which represents the inverse rate of the exponential decay of the density in the atmosphere. This problem is well suited for the notion of equivalent conditions and the effect of the atmosphere on the sun is as a first approximation local. This approach leads to solve only equations set in the sun. We derive rigorously equivalent conditions up to the fourth order of approximation with respect to δ for the exact solution u. The construction of equivalent conditions is based on a multiscale expansion in power series of δ for u. Numerical simulations illustrate the theoretical results. Finally we measure the boundary layer phenomenon by introducing a characteristic length that turns out to depend on the mean curvature of the interface between the subdomains.< Leer menos

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Multiscale expansions

Boundary layer

Equivalent conditions

Helioseismology

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

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