Positivity-Preserving Finite Difference WENO Schemes with Constrained   Transport for Ideal Magnetohydrodynamic Equations
  In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high order positivity-preserving finite difference WENO methods for the ideal magnetohydrodynamic (MHD) equations. Our schemes, under the constrained transport (CT) framework, can achieve high order accuracy, a discrete divergence-free condition and positivity of the numerical solution simultaneously. Numerical examples in 1D, 2D and 3D are provided to demonstrate the performance of the proposed method. 
Andrew J. Christlieb, Yuan Liu, Qi Tang, Zhengfu Xu
math.NA