Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes (Communications in Computational Physics, 2018)
In this paper, we introduce a high-order accurate constrained transporttype finite volume method to solve ideal magnetohydrodynamic equations on two-dimensionaltriangular meshes. A new divergence-free WENO-based reconstructionmethod is developed to maintain exactly divergence-free evolution of the numericalmagnetic field. In this formulation, the normal component of the magnetic field at eachface of a triangle is reconstructed uniquely and with the desired order of accuracy. Additionally,a new weighted flux interpolation approach is also developed to computethe z-component of the electric field at vertices of grid cells. We also present numericalexamples to demonstrate the accuracy and robustness of the proposed scheme.