Degenerate anisotropic elliptic problems and magnetized plasma simulations

TL;DR

This paper introduces a numerical method for degenerate anisotropic elliptic problems that is flexible for arbitrary anisotropy directions and effective across different anisotropy strengths, applied to magnetized plasma modeling.

Contribution

The paper presents a novel numerical approach that handles arbitrary anisotropy directions without specialized coordinates, applicable to magnetized plasma simulations.

Findings

Method is accurate in strongly and mildly anisotropic regimes.

Applicable to Euler-Lorentz system in drift-fluid limit.

Handles arbitrary space-dependent anisotropy directions.

Abstract

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.