Geodesic
High order numerical methods for Vlasov-Poisson models of plasma sheaths
Valentin Ayot1 ; Mehdi Badsi2 ; Yann Barsamian3 ; Anaïs Crestetto2 ; Nicolas Crouseilles4 ; Michel Mehrenberger5 ; Averil Prost6 ; Christian Tayou-Fotso7
1 Institut de Mathématiques, CNRS, UMR 5251, Université de Bordeaux, France
2 Nantes Université, CNRS, Laboratoire de Mathématiques Jean Leray, LMJL, UMR 6629, F-44000 Nantes, France
3 École européenne de Bruxelles 1, Belgique
4 Inria (Mingus team), IRMAR UMR 6625 and ENS Rennes, Univ Rennes, France
5 I2M, CMI, UMR 7373, Aix-Marseille Université, France
6 LMI (EA 3226 - FR CNRS 3335), INSA de Rouen, France
7 Labo. J. A. Dieudonné, UMR 6621, Université Nice-Sophia Antipolis, France
ESAIM. Proceedings, Tome 77 (2024), pp. 229-248.

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This article is a report of the CEMRACS 2022 project, called HIVLASHEA, standing for ”High order methods for Vlasov-Poisson models for sheaths”. A two-species Vlasov-Poisson model is described together with some numerical simulations, permitting to exhibit the formation of a plasma sheath. The numerical simulations are performed with two different methods: a first order classical finite difference (FD) scheme and a high order semi-Lagrangian (SL) scheme with Strang splitting; for the latter one, the implementation of (non-periodic) boundary conditions is discussed and different solvers for the electric field are compared. The codes are first evaluated on a one-species case, where an analytical solution is known. For the two-species case, cross-comparisons are performed and the numerical convergence of the SL method is investigated. The use of high order method is emphasized in this context. The (parallel) SL code turns out to be a robust tool to provide reliable numerical approximations of sheath stationary solution with realistic physical parameters.
DOI : 10.1051/proc/202477229

Valentin Ayot 1 ; Mehdi Badsi 2 ; Yann Barsamian 3 ; Anaïs Crestetto 2 ; Nicolas Crouseilles 4 ; Michel Mehrenberger 5 ; Averil Prost 6 ; Christian Tayou-Fotso 7

1 Institut de Mathématiques, CNRS, UMR 5251, Université de Bordeaux, France
2 Nantes Université, CNRS, Laboratoire de Mathématiques Jean Leray, LMJL, UMR 6629, F-44000 Nantes, France
3 École européenne de Bruxelles 1, Belgique
4 Inria (Mingus team), IRMAR UMR 6625 and ENS Rennes, Univ Rennes, France
5 I2M, CMI, UMR 7373, Aix-Marseille Université, France
6 LMI (EA 3226 - FR CNRS 3335), INSA de Rouen, France
7 Labo. J. A. Dieudonné, UMR 6621, Université Nice-Sophia Antipolis, France 
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     author = {Valentin Ayot and Mehdi Badsi and Yann Barsamian and Ana{\"\i}s Crestetto and Nicolas Crouseilles and Michel Mehrenberger and Averil Prost and Christian Tayou-Fotso},
     title = {High order numerical methods for {Vlasov-Poisson} models of plasma sheaths},
     journal = {ESAIM. Proceedings},
     pages = {229--248},
     publisher = {mathdoc},
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     year = {2024},
     doi = {10.1051/proc/202477229},
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     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/proc/202477229/}
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Valentin Ayot; Mehdi Badsi; Yann Barsamian; Anaïs Crestetto; Nicolas Crouseilles; Michel Mehrenberger; Averil Prost; Christian Tayou-Fotso. High order numerical methods for Vlasov-Poisson models of plasma sheaths. ESAIM. Proceedings, Tome 77 (2024), pp. 229-248. doi : 10.1051/proc/202477229. https://geodesic-test.mathdoc.fr/articles/10.1051/proc/202477229/

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