Numerical modeling of oscillations for axisymmetric solar backgrounds with differential rotation and gravity
Abstract
In the context of local helioseismology, we present a robust numerical framework based on the Hybridizable Discontinuous Galerkin (HDG) method for solving the linearized equations of stellar oscillations in realistic solar backgrounds, incorporating gravity, stratification, differential rotation, and acoustic attenuation. The governing equations are formulated using the displacement vector and the pressure perturbation as the unknowns and are solved in the frequency domain. The time-independent background model is assumed to be axisymmetric, allowing for a decomposition into azimuthal Fourier modes at each frequency. This leads to a set of 2D decoupled equations in Fourier space, which are numerically solved with the HDG method. We investigate the response to external sources of excitation, particularly Dirac-type sources. At low attenuation levels, we observe the emergence of complex singularity structures (for example in the near-surface layers and in the solar atmosphere). This behaviour follows from the propagation of singularities principles, since in the absence of attenuation the problem is of mixed elliptic-hyperbolic type. To maintain accuracy at small (solar-like) attenuation levels, we develop an HDG stabilization strategy. Our numerical experiments illustrate the accuracy and robustness of the proposed HDG formulation. Our Green's function calculations achieve the high level of accuracy required by passive imaging methods in helioseismology. In particular, we show that the mode frequencies and the rotational splitting coefficients due to differential rotation extracted from the model power spectrum are consistent with solar observations at a level of accuracy better than a tenth of a nanohertz.
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BibTeX
@article{pham2026numerical,
title = {{Numerical modeling of oscillations for axisymmetric solar backgrounds with differential rotation and gravity}},
author = {Ha Pham and Florian Faucher and Damien Fournier and Hélène Barucq and Laurent Gizon},
journal = {Journal of Computational Physics},
year = {2026},
month = nov,
doi = {10.1016/j.jcp.2026.115506},
url = {https://inria.hal.science/hal-05847256v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Numerical modeling of oscillations for axisymmetric solar backgrounds with differential rotation and gravity
AU - Ha Pham
AU - Florian Faucher
AU - Damien Fournier
AU - Hélène Barucq
AU - Laurent Gizon
PY - 2026
DA - 2026/11/01
JO - Journal of Computational Physics
DO - 10.1016/j.jcp.2026.115506
UR - https://inria.hal.science/hal-05847256v1
AB - In the context of local helioseismology, we present a robust numerical framework based on the Hybridizable Discontinuous Galerkin (HDG) method for solving the linearized equations of stellar oscillations in realistic solar backgrounds, incorporating gravity, stratification, differential rotation, and acoustic attenuation. The governing equations are formulated using the displacement vector and the pressure perturbation as the unknowns and are solved in the frequency domain. The time-independent background model is assumed to be axisymmetric, allowing for a decomposition into azimuthal Fourier modes at each frequency. This leads to a set of 2D decoupled equations in Fourier space, which are numerically solved with the HDG method. We investigate the response to external sources of excitation, particularly Dirac-type sources. At low attenuation levels, we observe the emergence of complex singularity structures (for example in the near-surface layers and in the solar atmosphere). This behaviour follows from the propagation of singularities principles, since in the absence of attenuation the problem is of mixed elliptic-hyperbolic type. To maintain accuracy at small (solar-like) attenuation levels, we develop an HDG stabilization strategy. Our numerical experiments illustrate the accuracy and robustness of the proposed HDG formulation. Our Green's function calculations achieve the high level of accuracy required by passive imaging methods in helioseismology. In particular, we show that the mode frequencies and the rotational splitting coefficients due to differential rotation extracted from the model power spectrum are consistent with solar observations at a level of accuracy better than a tenth of a nanohertz.
SN - 0021-9991
SN - 1090-2716
ER -