A CWENO-type central-upwind scheme for ideal MHD equations

A simple fourth-order, central-upwind scheme based on central weighted essentially non-oscillatory (CWENO) reconstruction is proposed in this paper for computing the approximate solutions of one- and two-dimensional ideal magnetohydrodynamics (MHD) equations with high-resolution. Since the non-uniform width of the different local Riemann fans is calculated more accurately, the central-upwind schemes enjoy a much smaller numerical viscosity as well as the staggering between two neighboring sets of grids is avoided. Due to the central-upwind scheme is combined with the fourth-order CWENO reconstruction, the scheme we present has the non-oscillatory behavior. The numerical results show the desired accuracy, high-resolution, and robustness of our method.