1,575 research outputs found
An asymptotic preserving scheme for strongly anisotropic elliptic problems
In this article we introduce an asymptotic preserving scheme designed to
compute the solution of a two dimensional elliptic equation presenting large
anisotropies. We focus on an anisotropy aligned with one direction, the
dominant part of the elliptic operator being supplemented with Neumann boundary
conditions. A new scheme is introduced which allows an accurate resolution of
this elliptic equation for an arbitrary anisotropy ratio.Comment: 21 page
Degenerate anisotropic elliptic problems and magnetized plasma simulations
This paper is devoted to the numerical approximation of a degenerate
anisotropic elliptic problem. The numerical method is designed for arbitrary
space-dependent anisotropy directions and does not require any specially
adapted coordinate system. It is also designed to be equally accurate in the
strongly and the mildly anisotropic cases. The method is applied to the
Euler-Lorentz system, in the drift-fluid limit. This system provides a model
for magnetized plasmas
Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations
The present paper introduces an efficient and accurate numerical scheme for
the solution of a highly anisotropic elliptic equation, the anisotropy
direction being given by a variable vector field. This scheme is based on an
asymptotic preserving reformulation of the original system, permitting an
accurate resolution independently of the anisotropy strength and without the
need of a mesh adapted to this anisotropy. The counterpart of this original
procedure is the larger system size, enlarged by adding auxiliary variables and
Lagrange multipliers. This Asymptotic-Preserving method generalizes the method
investigated in a previous paper [arXiv:0903.4984v2] to the case of an
arbitrary anisotropy direction field
Degenerate anisotropic elliptic problems and magnetized plasma simulations.
International audienceThis paper is devoted to the numerical approximation of a degen- erate anisotropic elliptic problem. The numerical method is designed for arbitrary space-dependent anisotropy directions and does not re- quire any specially adapted coordinate system. It is also designed to be equally accurate in the strongly and the mildly anisotropic cases. The method is applied to the Euler-Lorentz system, in the drift-fluid limit. This system provides a model for magnetized plasmas
Asymptotic-Preserving scheme for a bi-fluid Euler-Lorentz model
The present work is devoted to the simulation of a strongly magnetized plasma
considered as a mixture of an ion fluid and an electron fluid. For the sake of
simplicity, we assume that the model is isothermal and described by Euler
equations coupled with a term representing the Lorentz force. Moreover we
assume that both Euler systems are coupled through a quasi-neutrality
constraint. The numerical method which is described in the present document is
based on an Asymptotic-Preserving semi-discretization in time of a variant of
this two-fluid Euler-Lorentz model with a small perturbation of the
quasi-neutrality constraint. Firstly, we present the two-fluid model and the
motivations for introducing a small perturbation into the quasi-neutrality
equation, then we describe the time semi-discretization of the perturbed model
and a fully-discrete finite volume scheme based on it. Finally, we present some
numerical results which have been obtained with this method
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