A Multistate Low-dissipation Advection Upstream Splitting Method for Ideal Magnetohydrodynamics
A Multistate Low-dissipation Advection Upstream Splitting Method for Ideal Magnetohydrodynamics
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DOI：
10.3847/1538-4365/ab8aee
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
T. Minoshima;K. Kitamura;T. Miyoshi
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文献类型：
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作者：
T. Minoshima;K. Kitamura;T. Miyoshi
提出了一种新的理想磁流体力学(MHD)数值模拟格式，该格式对一维和多维激波具有较强的稳健性，对低马赫数流动和不连续流具有较高的精度。该格式属于计算空气动力学中的对流上游分裂方法，它将MHD方程中的无粘通量分解为平流、压力和磁张力部分，然后分别计算计算单元界面上的质量、压力和磁张力通量。质量通量的设计是为了避免多维的数值激波不稳定性，同时保持接触的不连续性。对于低马赫数流动，压力通量具有适当的标度，从而可以可靠地模拟几乎不可压缩的流动。为了保持旋转不连续性，建立了与HLLD近似黎曼解算器一致的磁张力通量。我们通过各种基准测试来验证该方案的新颖性能。我们的结果表明，对于同时包含低和高马赫数流动以及磁场不均匀的天体物理系统，该方案一定是一个很有前途的工具。
We develop a new numerical scheme for ideal magnetohydrodynamic (MHD) simulations, which is robust against one- and multidimensional shocks, and is accurate for low Mach number flows and discontinuities. The scheme belongs to a family of the advection upstream splitting method employed in computational aerodynamics, and it splits the inviscid flux in MHD equations into advection, pressure, and magnetic tension parts, and then individually evaluates mass, pressure, and magnetic tension fluxes at the interface of a computational cell. The mass flux is designed to avoid numerical shock instability in multidimensions, while preserving contact discontinuity. The pressure flux possesses a proper scaling for low Mach number flows, allowing reliable simulations of nearly incompressible flows. The magnetic tension flux is built to be consistent with the HLLD approximate Riemann solver to preserve rotational discontinuity. We demonstrate various benchmark tests to verify the novel performance of the scheme. Our results indicate that the scheme must be a promising tool to tackle astrophysical systems that include both low and high Mach number flows, as well as magnetic field inhomogeneities.