A new locally divergence-free WLS-ENO scheme based on the positivity-preserving finite volume method for ideal MHD equations

In this paper, the WLS-ENO (Weighted-Least-Squares based Essentially Non-Oscillatory) reconstruction is modified to maintain the conservation of the cell average values. Furthermore, the divergence-free constraint is combined with the conservative WLS-ENO reconstruction, which can make the magnetic...

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Bibliographic Details
Published in:Journal of computational physics 2021-12, Vol.447, p.110694, Article 110694
Main Authors: Liu, Mengqing, Zhang, Man, Li, Caixia, Shen, Fang
Format: Article
Language:English
Subjects:
Computational physics
Divergence
Finite volume method
Locally divergence-free
Magnetic fields
Magnetic properties
Mathematical analysis
MHD
Reconstruction
WLS-ENO
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Summary:In this paper, the WLS-ENO (Weighted-Least-Squares based Essentially Non-Oscillatory) reconstruction is modified to maintain the conservation of the cell average values. Furthermore, the divergence-free constraint is combined with the conservative WLS-ENO reconstruction, which can make the magnetic field locally divergence-free. The main merit of the proposed reconstruction scheme is that it can keep both the divergence-free constraint and ENO property for the magnetic field without using any limiter. We apply the scheme to the simulations of ideal MHD equations within the framework of a positivity-preserving finite volume method. The convergence, the magnetic field divergence error and the capability for low plasma-beta of the scheme are tested by some MHD benchmark problems.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2021.110694