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

2014/06/19 by Andrew Christlieb, Christlieb, Andrew J., Yuan Liu +5 · 2 citations
Engineering · Mathematics · #35L65 #65M06 #65M20 #76W05 #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1406.5098

openalex publication_date 2014/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• An active-flux-type scheme for ideal MHD with provable positivity and discrete divergence-free property
• Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system

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