A New S-M Limiter Entropy Stable Scheme Based on Moving Mesh Method for Ideal MHD and SWMHD Equations

For magnetohydrodynamics (MHD) equations, the existing entropy stable (ES) flux effectively eliminates the spurious oscillation, but it still has potential for improvement such as the resolution of discontinuous solutions. We propose a high-resolution scheme based on a moving mesh strategy for appro...

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Bibliographic Details
Published in:Journal of scientific computing 2024-03, Vol.98 (3), p.68, Article 68
Main Authors: Zhai, Mengqing, Zheng, Supei, Zhang, Chengzhi, Jian, Mangmang
Format: Article
Language:English
Subjects:
Accretion disks
Algorithms
Astrophysics
Computational Mathematics and Numerical Analysis
Conservation laws
Design
Discontinuity
Dissipation
Entropy
Flow velocity
High resolution
Magnetic fields
Magnetohydrodynamics
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Mesh generation
Rarefaction
Robustness (mathematics)
Shallow water
Theoretical
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Summary:For magnetohydrodynamics (MHD) equations, the existing entropy stable (ES) flux effectively eliminates the spurious oscillation, but it still has potential for improvement such as the resolution of discontinuous solutions. We propose a high-resolution scheme based on a moving mesh strategy for approximating solutions of ideal MHD and shallow water MHD (SWMHD) in this paper. Firstly, a new S-M flux limiter is constructed to weigh the ES flux and the anti-diffusive flux to obtain a new flux with high resolution and entropy stability properties. By adjusting the amplitude of anti-diffusive flux adaptively, the new flux can reduce its dissipation in smooth regions and increase dissipation at discontinuities, which is more consistent with physical laws. Secondly, we introduce the moving mesh strategy to optimize mesh generation and eliminate the defects of structured mesh. A new monitor function is defined to identify structural features of solutions at each particular time level and to assign appropriate weights to all regions with large numerical solution gradients, to construct a mesh evolution equation and increase the mesh density of these regions. Finally, we combine the moving mesh strategy with the high-resolution ES scheme and evaluate more accurate solutions according to the order of “mesh redistribution-update of solution-equation solving on new mesh”. Numerical results show that the new algorithm can achieve strong robustness and high resolution, and can track various waves effectively (especially the shock and rarefaction waves).
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02458-9