A multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations
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.
Cite
@article{arxiv.2409.14992,
title = {A multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations},
author = {Pascal Tremblin and Rémi Bourgeois and Solène Bulteau and Samuel Kokh and Thomas Padioleau and Maxime Delorme and Antoine Strugarek and Matthias González and Allan Sacha Brun},
journal= {arXiv preprint arXiv:2409.14992},
year = {2024}
}
Comments
accepted in JCP