A split-step Active Flux method for the Vlasov-Poisson system
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913603003613184 |
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| author | Hensel, Lukas Grünwald, Gudrun Kormann, Katharina Grauer, Rainer |
| author_facet | Hensel, Lukas Grünwald, Gudrun Kormann, Katharina Grauer, Rainer |
| contents | Active Flux is a modified Finite Volume method that evolves additional Degrees of Freedom for each cell that are located on the interface by a non-conservative method to compute high-order approximations to the numerical fluxes through the respective interface to evolve the cell-average in a conservative way. In this paper, we apply the method to the Vlasov-Poisson system describing the time evolution of the time-dependent distribution function of a collisionless plasma. In particular, we consider the evaluation of the flux integrals in higher dimensions. We propose a dimensional splitting and three types of formulations of the flux integral: a one-dimensional reconstruction of second order, a third-order reconstruction based on information along each dimension, and a third-order reconstruction based on a discrepancy formulation of the Active Flux method. Numerical results in 1D1V phase-space compare the properties of the various methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06525 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A split-step Active Flux method for the Vlasov-Poisson system Hensel, Lukas Grünwald, Gudrun Kormann, Katharina Grauer, Rainer Numerical Analysis Plasma Physics Active Flux is a modified Finite Volume method that evolves additional Degrees of Freedom for each cell that are located on the interface by a non-conservative method to compute high-order approximations to the numerical fluxes through the respective interface to evolve the cell-average in a conservative way. In this paper, we apply the method to the Vlasov-Poisson system describing the time evolution of the time-dependent distribution function of a collisionless plasma. In particular, we consider the evaluation of the flux integrals in higher dimensions. We propose a dimensional splitting and three types of formulations of the flux integral: a one-dimensional reconstruction of second order, a third-order reconstruction based on information along each dimension, and a third-order reconstruction based on a discrepancy formulation of the Active Flux method. Numerical results in 1D1V phase-space compare the properties of the various methods. |
| title | A split-step Active Flux method for the Vlasov-Poisson system |
| topic | Numerical Analysis Plasma Physics |
| url | https://arxiv.org/abs/2412.06525 |