A Locally Divergence-Free Local Characteristic Decomposition Based Path-Conservative Central-Upwind Scheme for Ideal Magnetohydrodynamics

TL;DR

This paper presents a novel low-dissipation numerical scheme for ideal magnetohydrodynamics that maintains divergence-free magnetic fields, improving solution accuracy in benchmark tests.

Contribution

It introduces a locally divergence-free characteristic decomposition into a path-conservative central-upwind scheme for MHD, reducing dissipation and enhancing resolution.

Findings

Enhanced resolution in benchmark tests

Reduced numerical dissipation

Maintains divergence-free magnetic fields

Abstract

We introduce a locally divergence-free local characteristic decomposition based path-conservative central-upwind (LCD-PCCU) scheme for ideal magnetohydrodynamics (MHD) equations. The proposed method is a low-dissipation extension of the recently proposed locally divergence-free PCCU scheme. To reduce the numerical dissipation, we incorporate the LCD into the PCCU framework. The resulting LCD-PCCU method enhances the resolution of numerical solutions as demonstrated through a series of benchmark tests.