Geodesic
Lagrangian/Eulerian solvers and simulations for Vlasov-Poisson
Sebastien Guisset1, 2 ; Michael Gutnic3, 4 ; Philippe Helluy3, 4 ; Michel Massaro4 ; Laurent Navoret3, 4 ; Nhung Pham3, 4 ; Malcolm Roberts3, 4
1 Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France
2 Univ. Bordeaux, IMB,UMR 5251, F- 33400 Talence, France
3 INRIA Nancy - Grand Est / IRMA - TONUS
4 IRMA, UMR 7501, Univ. de Strasbourg et CNRS
ESAIM. Proceedings, Tome 53 (2016), pp. 120-132.

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We construct a hyperbolic approximation of the Vlasov equation using a method of reduction [10, 14, 22] in which the dependency on the velocity variable is removed. The reduction relies on a semi-discrete finite element approximation in the velocity variable. We apply Gauss-Lobatto numerical integration in velocity space, reducing the hyperbolic system to a system of transport equations for which the transport velocities are the Gauss-Lobatto points. The transport equations are coupled through a zero-order term that represents the electromagnetic forces. We solve the resulting system by a splitting approach: the homogeneous transport equations are solved by a split semi-Lagrangian method and the source term is applied independently. We also present preliminary comparisons with another transport solver based on the discontinuous Galerkin method.
DOI : 10.1051/proc/201653008

Sebastien Guisset 1, 2 ; Michael Gutnic 3, 4 ; Philippe Helluy 3, 4 ; Michel Massaro 4 ; Laurent Navoret 3, 4 ; Nhung Pham 3, 4 ; Malcolm Roberts 3, 4

1 Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France
2 Univ. Bordeaux, IMB,UMR 5251, F- 33400 Talence, France
3 INRIA Nancy - Grand Est / IRMA - TONUS
4 IRMA, UMR 7501, Univ. de Strasbourg et CNRS 
@article{EP_2016_53_a8,
     author = {Sebastien Guisset and Michael Gutnic and Philippe Helluy and Michel Massaro and Laurent Navoret and Nhung Pham and Malcolm Roberts},
     title = {Lagrangian/Eulerian solvers and simulations for {Vlasov-Poisson}},
     journal = {ESAIM. Proceedings},
     pages = {120--132},
     publisher = {mathdoc},
     volume = {53},
     year = {2016},
     doi = {10.1051/proc/201653008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201653008/}
}
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Sebastien Guisset; Michael Gutnic; Philippe Helluy; Michel Massaro; Laurent Navoret; Nhung Pham; Malcolm Roberts. Lagrangian/Eulerian solvers and simulations for Vlasov-Poisson. ESAIM. Proceedings, Tome 53 (2016), pp. 120-132. doi : 10.1051/proc/201653008. http://geodesic.mathdoc.fr/articles/10.1051/proc/201653008/

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