Entropy stable numerical schemes for divergence diminishing Chew, Goldberger & Low equations for plasma flows

TL;DR

This paper develops entropy-stable numerical schemes for the GLM-CGL plasma flow model, effectively controlling magnetic field divergence and improving simulation stability compared to traditional CGL models.

Contribution

It introduces entropy-stable schemes for the GLM-CGL system, reformulating the equations to handle non-conservative terms without affecting entropy evolution.

Findings

The GLM approach significantly reduces magnetic field divergence.

Numerical results show improved stability over traditional CGL models.

The proposed methods maintain entropy stability in plasma flow simulations.

Abstract

Chew, Goldberger & Low (CGL) equations are a set of hyperbolic PDEs with non-conservative products used to model the plasma flows, when the assumption of local thermodynamic equilibrium is not valid, and the pressure tensor is assumed to be rotated by the magnetic field. This results in the pressure tensor, which is described by the two scalar components. As the magnetic field also evolves, controlling the divergence of the magnetic field is important. In this work, we consider the generalized Lagrange multiplier (GLM) technique for the CGL model. The resulting model is referred to as the GLM-CGL system. To make the system suitable for entropy-stable schemes, we reformulate the GLM-CGL system by treating some conservative terms as non-conservative. The resulting system has a non-conservative part that does not affect entropy evolution. We then propose entropy stable numerical methods for the GLM-CGL model. The numerical results for the GLM-CGL system are then compared with the CGL system without the GLM divergence diminishing approach to demonstrate that the GLM approach indeed leads to significant improvement in the magnetic field divergence diminishing.