### 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) |
---|---|

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 |

### Fingerprint

### 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

**Atmospheric radiation boundary conditions for the Helmholtz equation.** / Barucq, Hélène; Chabassier, Juliette; Duruflé, Marc; Gizon, Laurent; Leguèbe, Michael.

Research output: Contribution to journal › Article

*ESAIM: Mathematical Modelling and Numerical Analysis*, vol. 52, no. 3, pp. 945-964. https://doi.org/10.1051/m2an/2017059

}

TY - JOUR

T1 - Atmospheric radiation boundary conditions for the Helmholtz equation

AU - Barucq, Hélène

AU - Chabassier, Juliette

AU - Duruflé, Marc

AU - Gizon, Laurent

AU - Leguèbe, Michael

PY - 2018/5/1

Y1 - 2018/5/1

N2 - 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.

AB - 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.

KW - Atmosphere.

KW - Helmholtz equation

KW - Radiation boundary condition

UR - http://www.scopus.com/inward/record.url?scp=85047201979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047201979&partnerID=8YFLogxK

U2 - 10.1051/m2an/2017059

DO - 10.1051/m2an/2017059

M3 - Article

VL - 52

SP - 945

EP - 964

JO - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

SN - 0764-583X

IS - 3

ER -