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This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.
Barucq, Hélène 1 ; Chabassier, Juliette 1 ; Duruflé, Marc 1 ; Gizon, Laurent 1 ; Leguèbe, Michael 1
@article{M2AN_2018__52_3_945_0,
author = {Barucq, H\'el\`ene and Chabassier, Juliette and Durufl\'e, Marc and Gizon, Laurent and Legu\`ebe, Michael},
title = {Atmospheric radiation boundary conditions for the {Helmholtz} equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {945--964},
publisher = {EDP-Sciences},
volume = {52},
number = {3},
year = {2018},
doi = {10.1051/m2an/2017059},
mrnumber = {3865554},
zbl = {1403.85001},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017059/}
}
TY - JOUR AU - Barucq, Hélène AU - Chabassier, Juliette AU - Duruflé, Marc AU - Gizon, Laurent AU - Leguèbe, Michael TI - Atmospheric radiation boundary conditions for the Helmholtz equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 945 EP - 964 VL - 52 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017059/ DO - 10.1051/m2an/2017059 LA - en ID - M2AN_2018__52_3_945_0 ER -
%0 Journal Article %A Barucq, Hélène %A Chabassier, Juliette %A Duruflé, Marc %A Gizon, Laurent %A Leguèbe, Michael %T Atmospheric radiation boundary conditions for the Helmholtz equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 945-964 %V 52 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017059/ %R 10.1051/m2an/2017059 %G en %F M2AN_2018__52_3_945_0
Barucq, Hélène; Chabassier, Juliette; Duruflé, Marc; Gizon, Laurent; Leguèbe, Michael. Atmospheric radiation boundary conditions for the Helmholtz equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 945-964. doi: 10.1051/m2an/2017059
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