POSITIVITY-PRESERVING FINITE DIFFERENCE WEIGHTED ENO 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 nonoscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high-order positivity-preserving finite difference WENO methods for the ideal magnetohydrodynamic equations. Our scheme, under the constrained transport framework, can achieve high-order accuracy, a discrete divergence-free condition, and positivity of the numerical solution simultaneously. Numerical examples in one, two, and three dimensions are provided to demonstrate the performance of the proposed method.