Positivity-preserving finite difference weighted ENO schemes with constrained transport for ideal magnetohydrodynamic equations

Document Type

Article

Publication Date

1-1-2015

Abstract

© 2015 Society for Industrial and Applied Mathematics. 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 posi-tivity of the numerical solution simultaneously. Numerical examples in one, two, and three dimensions are provided to demonstrate the performance of the proposed method.

Publication Title

SIAM Journal on Scientific Computing

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