Combining the hybrid mimetic mixed method with the Scharfetter-Gummel scheme for magnetised transport in plasmas

TL;DR

This paper introduces a new numerical scheme combining the hybrid mimetic mixed method with the Scharfetter-Gummel scheme to effectively simulate magnetised plasma transport, especially under high anisotropy conditions.

Contribution

It develops a hybrid numerical scheme that efficiently handles anisotropic diffusion and advection in magnetised plasma models, improving simulation accuracy and computational efficiency.

Findings

Effective handling of high anisotropy in plasma transport simulations

Numerical tests demonstrate scheme's robustness and applicability

Efficient implementation via static condensation

Abstract

In this paper, we propose a numerical scheme for fluid models of magnetised plasmas. One important feature of the numerical scheme is that it should be able to handle the anisotropy induced by the magnetic field. In order to do so, we propose the use of the hybrid mimetic mixed (HMM) scheme for diffusion. This is combined with a hybridised variant of the Scharfetter-Gummel (SG) scheme for advection. The proposed hybrid scheme can be implemented very efficiently via static condensation. Numerical tests are then performed to show the applicability of the combined HMM-SG scheme, even for highly anisotropic magnetic fields.