Solving the guiding-center model on a regular hexagonal mesh

Abstract

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.

On Time-Discretization of the 2d Euler Equation by a Symplectic Crouch-Grossman Integrator

“…Papers [9] and [12] investigate full-discretizations of the Guiding Center Model by, respectively, forward semi-Lagrangian methods and backward semi-Lagrangian methods. See also [13] and [18].…”

Guiding center simulations on curvilinear grids

“…We refer to [24] for more references on semi-Lagrangian schemes, motivations, context description and other validations of the code that is used for the simulations. We mention also the work on the SELHEX project [27], which is an alternative strategy allowing to avoid geometrical singularity of the Jacobian, as it is the case for example using polar mesh.…”