The positivity-preserving high-order semi-Lagrangian spectral volume method for Vlasov-Poisson equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909568345309184 |
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| author | Zhang, Xinyue Cai, Xiaofeng Cao, Waixiang |
| author_facet | Zhang, Xinyue Cai, Xiaofeng Cao, Waixiang |
| contents | In this paper, a novel high order semi-Lagrangian (SL) spectral volume (SV) method is proposed and studied for nonlinear Vlasov-Poisson (VP) simulations via operator splitting. The proposed algorithm combines both advantages of semi-Lagrangian and spectral volume approaches, exhibiting strong stability, robustness under large time steps, arbitrary high-order accuracy in space, local mass conservation, and positivity preservation. Numerical study of the SLSV method applied to the one-dimensional and two-dimensional transport equations, the Vlasov-Poisson system, the classical benchmark problems including Landau damping and two-stream instabilities is conducted, confirming the effectiveness, accuracy, and robustness of our algorithm in addressing complex nonlinear phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The positivity-preserving high-order semi-Lagrangian spectral volume method for Vlasov-Poisson equations Zhang, Xinyue Cai, Xiaofeng Cao, Waixiang Numerical Analysis In this paper, a novel high order semi-Lagrangian (SL) spectral volume (SV) method is proposed and studied for nonlinear Vlasov-Poisson (VP) simulations via operator splitting. The proposed algorithm combines both advantages of semi-Lagrangian and spectral volume approaches, exhibiting strong stability, robustness under large time steps, arbitrary high-order accuracy in space, local mass conservation, and positivity preservation. Numerical study of the SLSV method applied to the one-dimensional and two-dimensional transport equations, the Vlasov-Poisson system, the classical benchmark problems including Landau damping and two-stream instabilities is conducted, confirming the effectiveness, accuracy, and robustness of our algorithm in addressing complex nonlinear phenomena. |
| title | The positivity-preserving high-order semi-Lagrangian spectral volume method for Vlasov-Poisson equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.04501 |