We introduce different high order time discretization schemes for backward semi-Lagrangian methods. These schemes are based on multi-step schemes like Adams-Moulton and Adams-Bashforth schemes combined with backward finite difference schemes. We apply these methods to transport equations for plasma physics applications and for the numerical simulation of instabilities in fluid mechanics. In the context of backward semi-Lagrangian methods, this time discretization strategy is particularly efficient and accurate when the spatial error discretization becomes negligeable and allows to use large time steps.
Abstract. This paper introduces a Semi-Lagrangian solver for the Vlasov-Poisson equations on a uniform hexagonal mesh. The latter is composed of equilateral triangles, thus it doesn't contain any singularities, unlike polar meshes. We focus on the guiding-center model, for which we need to develop a Poisson solver for the hexagonal mesh in addition to the Vlasov solver. For the interpolation step of the Semi-Lagrangian scheme, a comparison is made between the use of Box-splines and of Hermite finite elements. The code will be adapted to more complex models and geometries in the future.
Résumé. Dans cet article nous présentons un solveur semi-Lagrangien pour leséquations de Vlasov-Poisson sur un maillage hexagonal uniforme. Ce dernier est composé de triangleséquilatéraux, ainsi il ne présente aucune singularité, contrairement au maillage polaire. Nous nous concentrons ici sur le modèle centre-guide.À cette fin nous avons développé en plus du solveur pour Vlasov, un solveur de l'équation de Poisson pour maillage hexagonal. Nous comparons les résultats obtenus avec une interpolation paréléments finis d'Hermite et par des Box-splines. Dans l'avenir, ce code sera adaptéà des géométries et modèles plus complexes.
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