论文标题
高阶渐近保护有限的差异差异方案，在所有声音马赫数中，MHD方程的运输受限
High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers
论文作者
论文摘要
在本文中，提出了针对磁氢动力学（MHD）方程的高级半图像（SI）渐近保存（AP）和无差异有限差异基本非振荡（WENO）方案。我们考虑Sonic Mach Number $ \ Varepsilon $从$ 0 $到$ \ Mathcal {O}（1）$。通过SI隐式解释runge-kutta（IMEX-RK）时间离散化获得了高阶精度。通过具有特征性重建的有限差异差异方案来实现空间中的高阶精度。使用约束的运输方法来维持无分散差异的条件。我们正式证明该方案是AP。如果Si imex-RK方案的隐式部分僵化，则获得不可压缩MHD极限的渐近精度（AA）。提供了数值实验来验证我们提出的方法的AP，AA和无差异性能。此外，该方案可以很好地捕获不可压缩式的基本非振荡方式的不连续性，但它也是一个不可压缩的求解器，在低声音马赫限制下具有均匀的大型步骤条件。
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.
