A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system
In this work, we consider the numerical approximation of the two-species Vlasov-Poisson system using Eulerian methods. A family of exact non homogeneous stationary solutions are constructed using elliptic functions. Then, specific numerical schemes are proposed to compute solutions which remain clos...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2024-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2024/02/proc2407713.pdf |
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| _version_ | 1846139365913264128 |
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| author | Crouseilles Nicolas Lemou Mohammed Morel Guillaume Navaro Pierre |
| author_facet | Crouseilles Nicolas Lemou Mohammed Morel Guillaume Navaro Pierre |
| author_sort | Crouseilles Nicolas |
| collection | DOAJ |
| description | In this work, we consider the numerical approximation of the two-species Vlasov-Poisson system using Eulerian methods. A family of exact non homogeneous stationary solutions are constructed using elliptic functions. Then, specific numerical schemes are proposed to compute solutions which remain close to a given stationary solution since standard schemes fail to capture such a dynamics on coarse meshes. The strategy is based on a suitable decomposition of the solution (in the spirit of δ f approaches) which can be easily combined with any classical Vlasov solvers. For unstable dynamics, a projection technique is proposed in order to dynamically change the equilibrium. Finally, numerical tests are proposed to illustrate the good behavior of the proposed strategy. |
| format | Article |
| id | doaj-art-c54bf4102a8c4223bd1d179c4714c278 |
| institution | Kabale University |
| issn | 2267-3059 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj-art-c54bf4102a8c4223bd1d179c4714c2782024-12-06T10:47:34ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592024-01-017726728410.1051/proc/202477267proc2407713A well-balanced scheme using exact solutions to the two species Vlasov-Poisson systemCrouseilles Nicolas0Lemou Mohammed1Morel Guillaume2Navaro Pierre3Univ Rennes, Inria (Mingus team), IRMAR UMR 6625 and ENS RennesUniv Rennes, CNRS, IRMAR UMR 6625IMT AtlantiqueUniv Rennes, CNRS, Inria (Mingus team), IRMAR UMR 6625In this work, we consider the numerical approximation of the two-species Vlasov-Poisson system using Eulerian methods. A family of exact non homogeneous stationary solutions are constructed using elliptic functions. Then, specific numerical schemes are proposed to compute solutions which remain close to a given stationary solution since standard schemes fail to capture such a dynamics on coarse meshes. The strategy is based on a suitable decomposition of the solution (in the spirit of δ f approaches) which can be easily combined with any classical Vlasov solvers. For unstable dynamics, a projection technique is proposed in order to dynamically change the equilibrium. Finally, numerical tests are proposed to illustrate the good behavior of the proposed strategy.https://www.esaim-proc.org/articles/proc/pdf/2024/02/proc2407713.pdf |
| spellingShingle | Crouseilles Nicolas Lemou Mohammed Morel Guillaume Navaro Pierre A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system ESAIM: Proceedings and Surveys |
| title | A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system |
| title_full | A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system |
| title_fullStr | A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system |
| title_full_unstemmed | A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system |
| title_short | A well-balanced scheme using exact solutions to the two species Vlasov-Poisson system |
| title_sort | well balanced scheme using exact solutions to the two species vlasov poisson system |
| url | https://www.esaim-proc.org/articles/proc/pdf/2024/02/proc2407713.pdf |
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