A Locally Divergence-Free Local Characteristic Decomposition Based Path-Conservative Central-Upwind Scheme for Ideal Magnetohydrodynamics

2025/12/18 by Chu, Shaoshuai, Kurganov, Alexander, Lukacova-Medvidova, Maria +1
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2512.16346

openalex publication_date 2025/12/18 · openalex created_date 2025/12/21 · openalex updated_date 2026/07/28

Abstract

We introduce a locally divergence-free local characteristic decomposition based path-conservative central-upwind (LCD-PCCU) scheme for ideal magnetohydrodynamics (MHD) equations. The proposed method is a low-dissipation extension of the recently proposed locally divergence-free PCCU scheme. To reduce the numerical dissipation, we incorporate the LCD into the PCCU framework. The resulting LCD-PCCU method enhances the resolution of numerical solutions as demonstrated through a series of benchmark tests.

Citations

• Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes
• A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics
• Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
• Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes

Related

• A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics
• Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes
• Structure-Preserving Oscillation-Eliminating Discontinuous Galerkin Schemes for Ideal MHD Equations: Locally Divergence-Free and Positivity-Preserving
• Divergence-Free Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Rotating Shallow Water Magnetohydrodynamics
• An explicit divergence-free DG method for incompressible magnetohydrodynamics