A globally divergence-free entropy stable nodal DG method for conservative ideal MHD equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912184422891520 |
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| author | Liu, Yuchang Guo, Wei Jiang, Yan Zhang, Mengping |
| author_facet | Liu, Yuchang Guo, Wei Jiang, Yan Zhang, Mengping |
| contents | We propose an arbitrarily high-order globally divergence-free entropy stable nodal discontinuous Galerkin (DG) method to directly solve the conservative form of the ideal MHD equations using appropriate quadrature rules. The method ensures a globally divergence-free magnetic field by updating it at interfaces with a constraint-preserving formulation [5] and employing a novel least-squares reconstruction technique. Leveraging this property, the semi-discrete nodal DG scheme is proven to be entropy stable. To handle the problems with strong shocks, we introduce a novel limiting strategy that suppresses unphysical oscillations while preserving the globally divergence-free property. Numerical experiments verify the accuracy and efficacy of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A globally divergence-free entropy stable nodal DG method for conservative ideal MHD equations Liu, Yuchang Guo, Wei Jiang, Yan Zhang, Mengping Numerical Analysis We propose an arbitrarily high-order globally divergence-free entropy stable nodal discontinuous Galerkin (DG) method to directly solve the conservative form of the ideal MHD equations using appropriate quadrature rules. The method ensures a globally divergence-free magnetic field by updating it at interfaces with a constraint-preserving formulation [5] and employing a novel least-squares reconstruction technique. Leveraging this property, the semi-discrete nodal DG scheme is proven to be entropy stable. To handle the problems with strong shocks, we introduce a novel limiting strategy that suppresses unphysical oscillations while preserving the globally divergence-free property. Numerical experiments verify the accuracy and efficacy of our method. |
| title | A globally divergence-free entropy stable nodal DG method for conservative ideal MHD equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.06815 |