A multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations
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arXiv
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| Autores principales: | , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914955204231168 |
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| author | Tremblin, Pascal Bourgeois, Rémi Bulteau, Solène Kokh, Samuel Padioleau, Thomas Delorme, Maxime Strugarek, Antoine González, Matthias Brun, Allan Sacha |
| author_facet | Tremblin, Pascal Bourgeois, Rémi Bulteau, Solène Kokh, Samuel Padioleau, Thomas Delorme, Maxime Strugarek, Antoine González, Matthias Brun, Allan Sacha |
| contents | We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is not entropy satisfying but is observed experimentally to be more robust than standard constrained transport schemes at low plasma beta. At very low plasma beta and high Alfvén number, we have designed an entropy-satisfying version that is not conservative for the magnetic field but preserves admissible states and we switch locally a-priori between the two versions depending on the regime of plasma beta and Alfvén number. This strategy is robust in a wide range of standard MHD test cases, all performed at second order with a classic MUSCL-Hancock scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14992 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations Tremblin, Pascal Bourgeois, Rémi Bulteau, Solène Kokh, Samuel Padioleau, Thomas Delorme, Maxime Strugarek, Antoine González, Matthias Brun, Allan Sacha Computational Physics Instrumentation and Methods for Astrophysics Plasma Physics We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is not entropy satisfying but is observed experimentally to be more robust than standard constrained transport schemes at low plasma beta. At very low plasma beta and high Alfvén number, we have designed an entropy-satisfying version that is not conservative for the magnetic field but preserves admissible states and we switch locally a-priori between the two versions depending on the regime of plasma beta and Alfvén number. This strategy is robust in a wide range of standard MHD test cases, all performed at second order with a classic MUSCL-Hancock scheme. |
| title | A multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations |
| topic | Computational Physics Instrumentation and Methods for Astrophysics Plasma Physics |
| url | https://arxiv.org/abs/2409.14992 |