Toward High-order Solar Corona Simulations: A High-order Hyperbolized Poisson Approach for Magnetic Field Initialization
Proper initialization of the solar corona magnetic field is important for easing the iterative process of realistic and efficient global magnetohydrodynamics (MHD) simulations. This study introduces a high-order flux reconstruction (FR) framework for solving the Poisson equation, a necessary step fo...
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| Format: | Article |
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IOP Publishing
2025-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/adace5 |
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| author | Rayan Dhib Firas Ben Ameur Vatsalya Sharma Andrea Lani Stefaan Poedts |
| author_facet | Rayan Dhib Firas Ben Ameur Vatsalya Sharma Andrea Lani Stefaan Poedts |
| author_sort | Rayan Dhib |
| collection | DOAJ |
| description | Proper initialization of the solar corona magnetic field is important for easing the iterative process of realistic and efficient global magnetohydrodynamics (MHD) simulations. This study introduces a high-order flux reconstruction (FR) framework for solving the Poisson equation, a necessary step for computing a potential-field source-surface (PFSS) to initialize the magnetic field for global solar corona simulations with MHD. By hyperbolizing the elliptic Poisson equation into a set of hyperbolic equations, we develop an efficient and robust high-order PFSS solver. Our contributions include developing a Q 2 (i.e., quadratic) geometrical representation using prismatic elements for the computational domain, which enables high-order mesh generation. Such a hyperbolized Poisson solver effectively relaxes magnetic fields extrapolated from solar magnetograms, producing scalar potential fields that align well with theoretical expectations. Extensive verification was conducted on the high-order FR solver for polynomial orders up to P 3, achieving fourth-order spatial accuracy. The hyperbolized solver demonstrates comparable accuracy to reference solutions (both analytical and numerical) while offering efficient performance, particularly on coarser meshes, making it competitive with state-of-the-art low-order finite volume solvers, which are mostly used for solar MHD simulations. The described developments are a milestone for enabling high-order global solar corona simulations on 3D unstructured grids. |
| format | Article |
| id | doaj-art-61abdf2c8d6f44639462b4fd851653c3 |
| institution | Kabale University |
| issn | 1538-4357 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj-art-61abdf2c8d6f44639462b4fd851653c32025-02-12T06:40:36ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-01980216310.3847/1538-4357/adace5Toward High-order Solar Corona Simulations: A High-order Hyperbolized Poisson Approach for Magnetic Field InitializationRayan Dhib0https://orcid.org/0000-0003-3670-4678Firas Ben Ameur1https://orcid.org/0000-0001-5097-2885Vatsalya Sharma2https://orcid.org/0000-0003-2781-6563Andrea Lani3https://orcid.org/0000-0003-4017-215XStefaan Poedts4https://orcid.org/0000-0002-1743-0651Centre for Mathematical Plasma-Astrophysics , KU Leuven, Celestijnenlaan 200-B, 3001 Leuven, Belgium ; rayan.dhib@kuleuven.be, vatsalya.sharma@kuleuven.be, andrea.lani@kuleuven.be, stefaan.poedts@kuleuven.beKing Abdullah University of Science and Technology , KSA-23955 Thuwal, Saudi Arabia ; firas.benameur@kaust.edu.saCentre for Mathematical Plasma-Astrophysics , KU Leuven, Celestijnenlaan 200-B, 3001 Leuven, Belgium ; rayan.dhib@kuleuven.be, vatsalya.sharma@kuleuven.be, andrea.lani@kuleuven.be, stefaan.poedts@kuleuven.beCentre for Mathematical Plasma-Astrophysics , KU Leuven, Celestijnenlaan 200-B, 3001 Leuven, Belgium ; rayan.dhib@kuleuven.be, vatsalya.sharma@kuleuven.be, andrea.lani@kuleuven.be, stefaan.poedts@kuleuven.beCentre for Mathematical Plasma-Astrophysics , KU Leuven, Celestijnenlaan 200-B, 3001 Leuven, Belgium ; rayan.dhib@kuleuven.be, vatsalya.sharma@kuleuven.be, andrea.lani@kuleuven.be, stefaan.poedts@kuleuven.be; Institute of Physics, University of Maria Curie-Skłodowska , ul. Radziszewskiego 10, PL-20-031 Lublin, PolandProper initialization of the solar corona magnetic field is important for easing the iterative process of realistic and efficient global magnetohydrodynamics (MHD) simulations. This study introduces a high-order flux reconstruction (FR) framework for solving the Poisson equation, a necessary step for computing a potential-field source-surface (PFSS) to initialize the magnetic field for global solar corona simulations with MHD. By hyperbolizing the elliptic Poisson equation into a set of hyperbolic equations, we develop an efficient and robust high-order PFSS solver. Our contributions include developing a Q 2 (i.e., quadratic) geometrical representation using prismatic elements for the computational domain, which enables high-order mesh generation. Such a hyperbolized Poisson solver effectively relaxes magnetic fields extrapolated from solar magnetograms, producing scalar potential fields that align well with theoretical expectations. Extensive verification was conducted on the high-order FR solver for polynomial orders up to P 3, achieving fourth-order spatial accuracy. The hyperbolized solver demonstrates comparable accuracy to reference solutions (both analytical and numerical) while offering efficient performance, particularly on coarser meshes, making it competitive with state-of-the-art low-order finite volume solvers, which are mostly used for solar MHD simulations. The described developments are a milestone for enabling high-order global solar corona simulations on 3D unstructured grids.https://doi.org/10.3847/1538-4357/adace5Computational methodsSolar coronaSpace weather |
| spellingShingle | Rayan Dhib Firas Ben Ameur Vatsalya Sharma Andrea Lani Stefaan Poedts Toward High-order Solar Corona Simulations: A High-order Hyperbolized Poisson Approach for Magnetic Field Initialization The Astrophysical Journal Computational methods Solar corona Space weather |
| title | Toward High-order Solar Corona Simulations: A High-order Hyperbolized Poisson Approach for Magnetic Field Initialization |
| title_full | Toward High-order Solar Corona Simulations: A High-order Hyperbolized Poisson Approach for Magnetic Field Initialization |
| title_fullStr | Toward High-order Solar Corona Simulations: A High-order Hyperbolized Poisson Approach for Magnetic Field Initialization |
| title_full_unstemmed | Toward High-order Solar Corona Simulations: A High-order Hyperbolized Poisson Approach for Magnetic Field Initialization |
| title_short | Toward High-order Solar Corona Simulations: A High-order Hyperbolized Poisson Approach for Magnetic Field Initialization |
| title_sort | toward high order solar corona simulations a high order hyperbolized poisson approach for magnetic field initialization |
| topic | Computational methods Solar corona Space weather |
| url | https://doi.org/10.3847/1538-4357/adace5 |
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