Chew, Goldberger & Low Equations: Eigensystem Analysis and Applications to One-Dimensional Test Problems
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913781488025600 |
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| author | Singh, Chetan Bhoriya, Deepak Yadav, Anshu Kumar, Harish Balsara, Dinshaw S. |
| author_facet | Singh, Chetan Bhoriya, Deepak Yadav, Anshu Kumar, Harish Balsara, Dinshaw S. |
| contents | Chew, Goldberger & Low (CGL) equations describe one of the simplest plasma flow models that allow anisotropic pressure, i.e., pressure is modeled using a symmetric tensor described by two scalar pressure components, one parallel to the magnetic field, another perpendicular to the magnetic field. The system of equations is a non-conservative hyperbolic system. In this work, we analyze the eigensystem of the CGL equations. We present the eigenvalues and the complete set of right eigenvectors. We also prove the linear degeneracy of some of the characteristic fields. Using the eigensystem for CGL equations, we propose HLL and HLLI Riemann solvers for the CGL system. Furthermore, we present the AFD-WENO schemes up to the seventh order in one dimension and demonstrate the performance of the schemes on several one-dimensional test cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chew, Goldberger & Low Equations: Eigensystem Analysis and Applications to One-Dimensional Test Problems Singh, Chetan Bhoriya, Deepak Yadav, Anshu Kumar, Harish Balsara, Dinshaw S. Numerical Analysis Mathematical Physics Chew, Goldberger & Low (CGL) equations describe one of the simplest plasma flow models that allow anisotropic pressure, i.e., pressure is modeled using a symmetric tensor described by two scalar pressure components, one parallel to the magnetic field, another perpendicular to the magnetic field. The system of equations is a non-conservative hyperbolic system. In this work, we analyze the eigensystem of the CGL equations. We present the eigenvalues and the complete set of right eigenvectors. We also prove the linear degeneracy of some of the characteristic fields. Using the eigensystem for CGL equations, we propose HLL and HLLI Riemann solvers for the CGL system. Furthermore, we present the AFD-WENO schemes up to the seventh order in one dimension and demonstrate the performance of the schemes on several one-dimensional test cases. |
| title | Chew, Goldberger & Low Equations: Eigensystem Analysis and Applications to One-Dimensional Test Problems |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2504.05503 |