• DOI:10.48550/arXiv.2211.16655
• Corpus ID: 254096106

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

@article{Chen2022HighOA,
  title={High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers},
  author={Wei Chen and Kailiang Wu and Tao Xiong},
  journal={ArXiv},
  year={2022},
  volume={abs/2211.16655}
}

• Wei Chen, Kailiang Wu, Tao Xiong
• Published 30 November 2022
• Computer Science
• ArXiv

In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for magnetohydrodynamic (MHD) equations. We consider the sonic Mach number $\varepsilon$ ranging from $0$ to $\mathcal{O}(1)$. High-order accuracy in time is obtained by SI implicit-explicit Runge-Kutta (IMEX-RK) time discretization. High-order accuracy in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions. A constrained transport method is applied to maintain a discrete divergence-free condition. We formally prove that the scheme is AP. Asymptotic accuracy (AA) in the incompressible MHD limit is obtained if the implicit part of the SI IMEX-RK scheme is stiffly accurate. Numerical experiments are provided to validate the AP, AA, and divergence-free properties of our proposed approach. Besides, the scheme can well capture discontinuities such as shocks in an essentially non-oscillatory fashion in the compressible regime, while it is also a good incompressible solver with uniform large-time step conditions in the low sonic Mach limit.