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 perform...

中文翻译：

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理想磁流体动力学的多态低耗散平流上游分裂方法

我们为理想的磁流体动力学（MHD）仿真开发了一种新的数值方案，该方案对一维和多维冲击具有鲁棒性，对于低马赫数流量和不连续性也很精确。该方案属于计算空气动力学中使用的对流上游分裂方法的一族，它将MHD方程中的无粘性通量分解为对流，压力和磁张力部分，然后分别评估质量，压力和磁张力通量。计算单元的接口。质量通量的设计可避免多维数值冲击不稳定性，同时保留接触间断。对于低马赫数的流量，压力通量具有适当的缩放比例，从而可以对几乎不可压缩的流量进行可靠的模拟。构造的磁力通量与HLLD近似Riemann求解器一致，以保持旋转不连续性。我们演示了各种基准测试，以验证这种新颖的性能。