We propose an arbitrarily high-order globally divergence-free entropy stable nodal discontinuous Galerkin (DG) method to directly solve the conservative form of the ideal MHD equations using appropriate quadrature rules. The method ensures a globally divergence-free magnetic field by updating it at interfaces with a constraint-preserving formulation [5] and employing a novel least-squares reconstruction technique. Leveraging this property, the semi-discrete nodal DG scheme is proven to be entropy stable. To handle the problems with strong shocks, we introduce a novel limiting strategy that suppresses unphysical oscillations while preserving the globally divergence-free property. Numerical experiments verify the accuracy and efficacy of our method.
@article{arxiv.2501.06815,
title = {A globally divergence-free entropy stable nodal DG method for conservative ideal MHD equations},
author = {Yuchang Liu and Wei Guo and Yan Jiang and Mengping Zhang},
journal= {arXiv preprint arXiv:2501.06815},
year = {2025}
}