We demonstrate the ability of nonoscillatory interpolation strategies for solving efficiently the transport phase in kinetic systems with applications to charged particle transport in plasmas and semiconductors. Pointwise weighted essentially nonoscillatory (PWENO) interpolation is applied to obtain semi-Lagrangian and flux balance methods that together with splitting techniques form the building blocks of our numerical approach. These methods do not present the restrictive CFL condition typical of finite-difference methods with explicit time-solvers, and, moreover, they provide reliable results controlling parasite oscillations from classical polynomial interpolation while giving highly accurate approximations of smooth parts of the solutions. We perform and compare these methods in different benchmark problems for Vlasov or collisional models for charged particle transport.
Abstract. We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.
Abstract. We present a discontinuous Galerkin scheme for the numerical approximation of the onedimensional periodic Vlasov-Poisson equation. The scheme is based on a Galerkin-characteristics method in which the distribution function is projected onto a space of discontinuous functions. We present comparisons with a semi-Lagrangian method to emphasize the good behavior of this scheme when applied to Vlasov-Poisson test cases.Résumé. Une méthode de Galerkin discontinu est proposée pour l'approximation numérique de l'équation de Vlasov-Poisson 1D. L'approche est basée sur une méthode Galerkin-caractéristiques où la fonction de distribution est projetée sur un espace de fonctions discontinues. En particulier, la méthode est comparéeà une méthode semi-Lagrangienne pour l'approximation de l'équation de Vlasov-Poisson.
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