Atmospheric radiation boundary conditions for the Helmholtz equation

Hélène Barucq, Juliette Chabassier, Marc Duruflé, Laurent Gizon, Michael Leguèbe

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)945-964
Number of pages20
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume52
Issue number3
DOIs
StatePublished - May 1 2018

Fingerprint

Atmospheric radiation
Radiation Boundary Conditions
Helmholtz equation
Helmholtz Equation
Atmosphere
Boundary conditions
Dirichlet-to-Neumann Map
Spherical coordinates
Acoustic Waves
Sun
Acoustic waves
Wave equation
Numerical Study
Incidence
Factorization
Radius
Decay
Wave equations
Angle
Configuration

Keywords

  • Atmosphere.
  • Helmholtz equation
  • Radiation boundary condition

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

Cite this

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

In: ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 52, No. 3, 01.05.2018, p. 945-964.

Research output: Contribution to journalArticle

Barucq, Hélène ; Chabassier, Juliette ; Duruflé, Marc ; Gizon, Laurent ; Leguèbe, Michael. / Atmospheric radiation boundary conditions for the Helmholtz equation. In: ESAIM: Mathematical Modelling and Numerical Analysis. 2018 ; Vol. 52, No. 3. pp. 945-964.
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