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

Abstract

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.

21 pages, 28 figures

References in corpus (1)

• Second Order Accurate Schemes for Magnetohydrodynamics With Divergence-Free Reconstruction

Cited by in corpus (3)

• High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
• A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations
• On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state