A simple, general framework is proposed to construct arbitrary order globally divergence-free discontinuous Galerkin (DG) scheme for ideal magnetohydrodynamic (MHD) equations on unstructured meshes. Similar to the approaches in [3, 41], our framework defines normal magnetic components on edges, updates them over time, and then uses these to reconstruct the globally divergence-free magnetic field. In particular, we design the 1D updating scheme for the normal magnetic component on each edge, and enhance the numerical flux selection to improve stability. Additionally, we achieve a significant improvement by utilizing mesh geometry and introducing variable substitution, resulting in a cell-independent reconstruction formulation that is both efficient and easy to implement. Numerical experiments confirm both the efficiency and effectiveness of our proposed method.
