A Modified Third-Order Semi-Discrete Central-Upwind Scheme for MHD Simulation

The Kurganov scheme is a third-order semi-discrete central numerical algorithm. The high solution of the scheme is ensured by a piecewise quadratic non-oscillatory reconstruction which consists of the cell-average data. We employ a modification of the smooth limiter of reconstruction in a simple way. The modified limiter possesses rigorous positivity and the reformulation does not change the non-oscillatory property of reconstruction. In order to explore the potential capability of application of the modified Kurganov scheme to magnetohydrodynamics (MHD) and resistive magnetohydrodynamics (RMHD) equations, two numerical problems are simulated in two dimensions (2D). These numerical simulations demonstrate that the modified Kurganov scheme keeps high precision and has stable reliable results for MHD and RMHD applications.