SLAU2-HLLD numerical flux with wiggle-sensor for stable low mach Magnetohydrodynamics simulations
SLAU2-HLLD numerical flux with wiggle-sensor for stable low mach Magnetohydrodynamics simulations
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DOI：
10.1016/j.compfluid.2021.105165
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发表时间：
2021-09
影响因子：
2.8
通讯作者：
Tomohiro Mamashita;K. Kitamura;T. Minoshima
中科院分区：
文献类型：
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作者：
Tomohiro Mamashita;K. Kitamura;T. Minoshima
SLAU 2（Simple Low-dissipation Advection-Upstream-splitting-method 2）是一种近似黎曼解算器，属于AUSM气体动力学格式家族。SLAU 2在超音速范围内稳定地捕获激波，并通过控制数值耗散在低速范围（马赫数0.01或更小）实现高分辨率。在以前的研究中，该方案被成功地扩展到磁流体动力学（MHD）模拟，如SLAU 2-HLL（SLAU 2-Harten-Lax-货车Leer）。然而，目前的研究表明，SLAU 2-HLL表现出非物理振荡在低速MHD测试。这个问题已被发现是由不足的数值耗散在磁场不连续性在低速范围内，因此，我们恢复的数值耗散只有在必要时通过引入一个摆动传感器功能的SLAU 2-HLL的压力通量的一部分。这一变化使SLAU 2-HLL能够计算低速磁流体动力学而不产生非物理振荡。此外，我们构造了SLAU 2-HLLD与HLLD（HLL-Discontinuity）的杂交，而不是HLL，它可以处理Alfvén波。通过将这种变化与摆动传感稳定方法相结合，我们成功地提高了原始SLAU 2-HLL的稳定性和低马赫MHD流的分辨率。使用一维和二维数值例子的修改的效果进行了演示。
SLAU2 (Simple Low-dissipation Advection-Upstream-splitting-method 2) is an approximate Riemann solver belonging to the AUSM family of schemes in gas dynamics. SLAU2 captures shock waves stably in a supersonic range and realizes high resolutions in the low-speed range (Mach number 0.01 or less) by controlling numerical dissipation. In a previous study, this scheme was successfully extended to magnetohydrodynamics (MHD) simulations, such as SLAU2-HLL (SLAU2-Harten–Lax–van Leer). However, the present study reveals that SLAU2-HLL exhibits unphysical oscillations in low-speed MHD tests. This problem has been found to be caused by insufficient numerical dissipation at the magnetic field discontinuity in a low speed range; thus, we recover the numerical dissipation only where necessary by introducing a wiggle sensor function to the pressure flux part of SLAU2-HLL. This change has enabled SLAU2-HLL to calculate low-speed MHD without unphysical oscillations. Furthermore, we constructed SLAU2-HLLD hybridized with HLLD (HLL-Discontinuity), instead of HLL, which can handle Alfvén waves. By combining this change with the wiggle-sensing stabilization method, we have succeeded in improving the stability and resolution for low Mach MHD flows from the original SLAU2-HLL. The effect of the modification is demonstrated using one- and two-dimensional numerical examples.