Assembling algorithm for Green's tensors and absorbing boundary conditions for Galbrun's equation in radial symmetry
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913492530888704 |
|---|---|
| author | Pham, Ha Faucher, Florian Fournier, Damien Barucq, Hélène Gizon, Laurent |
| author_facet | Pham, Ha Faucher, Florian Fournier, Damien Barucq, Hélène Gizon, Laurent |
| contents | Solar oscillations can be modeled by Galbrun's equation which describes Lagrangian wave displacement in a self-gravitating stratified medium. For spherically symmetric backgrounds, we construct an algorithm to compute efficiently and accurately the coefficients of the Green's tensor of the time-harmonic equation in vector spherical harmonic basis. With only two resolutions, our algorithm provides values of the kernels for all heights of source and receiver, and prescribes analytically the singularities of the kernels. We also derive absorbing boundary conditions (ABC) to model wave propagation in the atmosphere above the cut-off frequency. The construction of ABC, which contains varying gravity terms, is rendered difficult by the complex behavior of the solar potential in low atmosphere and for frequencies below the Lamb frequency. We carry out extensive numerical investigations to compare and evaluate the efficiency of the ABCs in capturing outgoing solutions. Finally, as an application towards helioseismology, we compute synthetic solar power spectra that contain pressure modes as well as internal-gravity (g-) and surface-gravity (f-) ridges which are missing in simpler approximations of the wave equation. For purpose of validation, the location of the ridges in the synthetic power spectra are compared with observed solar modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17080 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Assembling algorithm for Green's tensors and absorbing boundary conditions for Galbrun's equation in radial symmetry Pham, Ha Faucher, Florian Fournier, Damien Barucq, Hélène Gizon, Laurent Solar and Stellar Astrophysics Analysis of PDEs Solar oscillations can be modeled by Galbrun's equation which describes Lagrangian wave displacement in a self-gravitating stratified medium. For spherically symmetric backgrounds, we construct an algorithm to compute efficiently and accurately the coefficients of the Green's tensor of the time-harmonic equation in vector spherical harmonic basis. With only two resolutions, our algorithm provides values of the kernels for all heights of source and receiver, and prescribes analytically the singularities of the kernels. We also derive absorbing boundary conditions (ABC) to model wave propagation in the atmosphere above the cut-off frequency. The construction of ABC, which contains varying gravity terms, is rendered difficult by the complex behavior of the solar potential in low atmosphere and for frequencies below the Lamb frequency. We carry out extensive numerical investigations to compare and evaluate the efficiency of the ABCs in capturing outgoing solutions. Finally, as an application towards helioseismology, we compute synthetic solar power spectra that contain pressure modes as well as internal-gravity (g-) and surface-gravity (f-) ridges which are missing in simpler approximations of the wave equation. For purpose of validation, the location of the ridges in the synthetic power spectra are compared with observed solar modes. |
| title | Assembling algorithm for Green's tensors and absorbing boundary conditions for Galbrun's equation in radial symmetry |
| topic | Solar and Stellar Astrophysics Analysis of PDEs |
| url | https://arxiv.org/abs/2401.17080 |