A short note on reconstruction variables in shock capturing schemes for magnetohydrodynamics

TL;DR

This paper introduces simple approximate characteristic variables for shock capturing in MHD, improving robustness of reconstructions with comparable efficiency to traditional methods.

Contribution

It proposes a practical set of approximate characteristic variables that enhance robustness in high-order shock capturing schemes for MHD.

Findings

Reconstruction with approximate characteristic variables is more robust than using conservative or primitive variables.

Computational efficiency of the proposed variables is comparable to existing methods.

Numerical experiments validate the effectiveness of the approximate characteristic variables.

Abstract

We propose a set of quick and easy approximate characteristic variables for higher-order reconstructions of shock capturing schemes for magnetohydrodynamics (MHD). Numerical experiments suggest that the reconstructions using the approximate characteristic variables are more robust than those using the conservative or primitive variables, while their computational efficiencies are comparable. The approximate characteristic variables are simple compared to the full characteristic variables for MHD, and can be a practical choice of reconstruction variables.