Asymptotic-Preserving Schemes for Fluid Models of Plasmas

TL;DR

This paper discusses the development of Asymptotic-Preserving numerical schemes for plasma fluid models, capable of accurately handling a wide range of plasma parameters such as Debye length and cyclotron period.

Contribution

It introduces a framework for constructing schemes that remain valid across different regimes of plasma parameters, enhancing numerical stability and accuracy.

Findings

Schemes are valid for a large range of plasma parameters.

Framework enables application to various plasma problems.

Improves numerical robustness in plasma simulations.

Abstract

These notes summarize a series of works related to the numerical approximation of plasma fluid problems. We construct so-called 'Asymptotic-Preserving' schemes which are valid for a large range of values (from very small to order unity) of the dimensionless parameters that appear in plasma fluid models. Specifically, we are interested in two parameters, the scaled Debye length which quantifies how close to quasi-neutrality the plasma is, and the scaled cyclotron period, which is inversely proportional to the magnetic field strength. We will largely focus on the ideas, in order to enable the reader to apply these concepts to other situations.