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In this paper, we utilize the maximum-principle-preserving flux limitingtechnique, originally designed for high order weighted essentiallynon-oscillatory (WENO) methods for scalar hyperbolic conservation laws, todevelop a class of high order positivity-preserving finite difference WENOmethods for the ideal magnetohydrodynamic (MHD) equations. Our schemes, underthe constrained transport (CT) framework, can achieve high order accuracy, adiscrete divergence-free condition and positivity of the numerical solutionsimultaneously. Numerical examples in 1D, 2D and 3D are provided to demonstratethe performance of the proposed method.

Positivity-Preserving Finite Difference WENO Schemes with Constrained Transport for Ideal Magnetohydrodynamic Equations