An Arbitrarily High-order Spectral Difference Method with Divergence Cleaning (SDDC) for Compressible Magnetohydrodynamic Simulations on Unstructured Grids
An Arbitrarily High-order Spectral Difference Method with Divergence Cleaning (SDDC) for Compressible Magnetohydrodynamic Simulations on Unstructured Grids
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DOI：
10.3847/1538-4357/ac6e61
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Kuangxu Chen;C. Liang
中科院分区：
文献类型：
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作者：
Kuangxu Chen;C. Liang
本文报道了在由高阶等参四边形单元组成的曲线型非结构网格上精确模拟理想和阻性磁流体力学的高阶谱差分法(SDDC)的最新进展。散度清理方法是基于热力学上一致的改进的广义拉格朗日乘子。在光滑解的测试问题中，SDDC方法可以达到任意高精度的空间离散化。高阶SDDC方法与人工耗散方法相结合，能够很好地捕捉激波界面的无振荡特性，并能在相对稀疏的网格上分辨小尺度涡旋结构和密度起伏。通过对具有渐近相互作用激波结构的理想MHD问题、高Lundquist数的阻性MHD问题和复杂曲线域上的粘性阻性MHD问题的长时间模拟，证明了该程序的健壮性。
This paper reports a recent development of the high-order spectral difference method with divergence cleaning (SDDC) for accurate simulations of both ideal and resistive magnetohydrodynamics (MHD) on curved unstructured grids consisting of high-order isoparametric quadrilateral elements. The divergence cleaning approach is based on the improved generalized Lagrange multiplier, which is thermodynamically consistent. The SDDC method can achieve an arbitrarily high order of accuracy in spatial discretization, as demonstrated in the test problems with smooth solutions. The high-order SDDC method combined with the artificial dissipation method can sharply capture shock interfaces with the oscillation-free property and resolve small-scale vortex structures and density fluctuations on relatively sparse grids. The robustness of the codes is demonstrated through long time simulations of ideal MHD problems with progressively interacting shock structures, resistive MHD problems with high Lundquist numbers, and viscous resistive MHD problems on complex curved domains.