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Effect of the polarization drift in a strongly magnetized plasma

Daniel Han-Kwan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [SIAM J. Math. Anal. 32 (2001) 1227–1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in the...

Finite volume method in curvilinear coordinates for hyperbolic conservation laws⋆

A. Bonnement, T. Fajraoui, H. Guillard, M. Martin, A. Mouton, B. Nkonga, A. Sangam (2011)

ESAIM: Proceedings

This paper deals with the design of finite volume approximation of hyperbolic conservation laws in curvilinear coordinates. Such coordinates are encountered naturally in many problems as for instance in the analysis of a large number of models coming from magnetic confinement fusion in tokamaks. In this paper we derive a new finite volume method for hyperbolic conservation laws in curvilinear coordinates. The method is first described in a general...

Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis

Claire Chainais-Hillairet, Jian-Guo Liu, Yue-Jun Peng (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows us to deal...

Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis

Claire Chainais-Hillairet, Jian-Guo Liu, Yue-Jun Peng (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows us to deal...

Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case⋆

Pierre Degond, Fabrice Deluzet, Dario Maldarella, Jacek Narski, Claudia Negulescu, Martin Parisot (2011)

ESAIM: Proceedings

In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed...

Initial boundary value problem for generalized Zakharov equations

Shujun You, Boling Guo, Xiaoqi Ning (2012)

Applications of Mathematics

This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in ( 2 + 1 ) dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.

Limite quasi-neutre en dimension 1

Emmanuel Grenier (1999)

Journées équations aux dérivées partielles

L’objet de cette note est d’étudier la limite quasineutre des équations de Vlasov Poisson en dimension 1 d’espace. Ceci inclut l’obtention de résultats d’existence pour le système limite ainsi que la preuve de la convergence.

Numerical approximation of Knudsen layer for the Euler-Poisson system

Fréderique Charles, Nicolas Vauchelet, Christophe Besse, Thierry Goudon, Ingrid Lacroix–Violet, Jean-Paul Dudon, Laurent Navoret (2011)

ESAIM: Proceedings

In this work, we consider the computation of the boundary conditions for the linearized Euler–Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute numerically the boundary conditions in the hydrodynamic limit relying on an analysis of the boundary layers....

Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems

Jean-Michel Rakotoson, Maria Luisa Seoane (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations revelant from plasma physic problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.

On global solutions to a nonlinear Alfvén wave equation

XS. Feng, F. Wei (1995)

Annales Polonici Mathematici

We establish the global existence and uniqueness of smooth solutions to a nonlinear Alfvén wave equation arising in a finite-beta plasma. In addition, the spatial asymptotic behavior of the solution is discussed.

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