Geodesic
Solving the Vlasov equation in complex geometries
J. Abiteboul1 ; G. Latu1 ; V. Grandgirard1 ; A. Ratnani2 ; E. Sonnendrücker2 ; A. Strugarek1
1 CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
2 IRMA, Université de Strasbourg and INRIA-Nancy-Grand Est, CALVI Project-Team, France
ESAIM. Proceedings, Tome 32 (2011), pp. 103-117.

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This paper introduces an isoparametric analysis to solve the Vlasov equation with a semi-Lagrangian scheme. A Vlasov-Poisson problem modeling a heavy ion beam in an axisymmetric configuration is considered. Numerical experiments are conducted on computational meshes targeting different geometries. The impact of the computational grid on the accuracy and the computational cost are shown. The use of analytical mapping or Bézier patches does not induce a too large computational overhead and is quite accurate. This approach successfully couples an isoparametric analysis with a semi-Lagrangian scheme, and we expect to apply it to a gyrokinetic Vlasov solver.
DOI : 10.1051/proc/2011015

J. Abiteboul 1 ; G. Latu 1 ; V. Grandgirard 1 ; A. Ratnani 2 ; E. Sonnendrücker 2 ; A. Strugarek 1

1 CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
2 IRMA, Université de Strasbourg and INRIA-Nancy-Grand Est, CALVI Project-Team, France 
@article{EP_2011_32_a8,
     author = {J. Abiteboul and G. Latu and V. Grandgirard and A. Ratnani and E. Sonnendr\"ucker and A. Strugarek},
     title = {Solving the {Vlasov} equation in complex geometries},
     journal = {ESAIM. Proceedings},
     pages = {103--117},
     publisher = {mathdoc},
     volume = {32},
     year = {2011},
     doi = {10.1051/proc/2011015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2011015/}
}
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J. Abiteboul; G. Latu; V. Grandgirard; A. Ratnani; E. Sonnendrücker; A. Strugarek. Solving the Vlasov equation in complex geometries. ESAIM. Proceedings, Tome 32 (2011), pp. 103-117. doi : 10.1051/proc/2011015. http://geodesic.mathdoc.fr/articles/10.1051/proc/2011015/

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