A new locally divergence-free WLS-ENO scheme based on the positivity-preserving finite volume method for ideal MHD equations

In this paper, the WLS-ENO (Weighted-Least-Squares based Essentially Non-Oscillatory) reconstruction is modified to maintain the conservation of the cell average values. Furthermore, the divergence-free constraint is combined with the conservative WLS-ENO reconstruction, which can make the magnetic field locally divergence-free. The main merit of the proposed reconstruction scheme is that it can keep both the divergence-free constraint and ENO property for the magnetic field without using any limiter. We apply the scheme to the simulations of ideal MHD equations within the framework of a positivity-preserving finite volume method. The convergence, the magnetic field divergence error and the capability for low plasma-beta of the scheme are tested by some MHD benchmark problems.