### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 945-964 |

Number of pages | 20 |

Journal | ESAIM: Mathematical Modelling and Numerical Analysis |

Volume | 52 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2018 |

Externally published | Yes |

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### Keywords

- Atmosphere.
- Helmholtz equation
- Radiation boundary condition

### ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Modeling and Simulation
- Applied Mathematics

### Cite this

*ESAIM: Mathematical Modelling and Numerical Analysis*,

*52*(3), 945-964. https://doi.org/10.1051/m2an/2017059