A multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations

TL;DR

This paper introduces a new multi-dimensional, cell-centered finite-volume scheme for ideal MHD equations that is robust across various plasma regimes, combining relaxation, splitting, and adaptive strategies for improved stability and accuracy.

Contribution

The paper presents a novel multi-dimensional finite-volume scheme for ideal MHD that adapts between conservative and entropy-satisfying versions based on plasma conditions, enhancing robustness.

Findings

More robust than standard constrained transport schemes at low plasma beta.

Effective in a wide range of MHD test cases.

Achieves second-order accuracy with MUSCL-Hancock scheme.

Abstract

We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is not entropy satisfying but is observed experimentally to be more robust than standard constrained transport schemes at low plasma beta. At very low plasma beta and high Alfv\'en number, we have designed an entropy-satisfying version that is not conservative for the magnetic field but preserves admissible states and we switch locally a-priori between the two versions depending on the regime of plasma beta and Alfv\'en number. This strategy is robust in a wide range of standard MHD test cases, all performed at second order with a classic MUSCL-Hancock scheme.