Magnetic induction and electric potential smoothed particle magnetohydrodynamics for incompressible flows
Magnetic induction and electric potential smoothed particle magnetohydrodynamics for incompressible flows
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DOI：
10.1002/fld.4906
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发表时间：
2020-08
影响因子：
1.8
通讯作者：
Jabir Al-Salami;Changhong Hu;Mohamed M. Kamra;K. Hanada
中科院分区：
文献类型：
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作者：
Jabir Al-Salami;Changhong Hu;Mohamed M. Kamra;K. Hanada
为了求解不可压缩的非理想磁流体自由表面流动，建立了两种弱可压缩光滑粒子流体动力学模型，分别考虑了磁感应强度和不考虑磁感应强度。磁感应磁流体动力学（SPMHD）的SPH公式在天体物理学研究中很流行，它首次被应用于不可压缩自由表面MHD流动，如液态金属流动，考虑了非理想MHD效应和具有任意电导率的边界。一个SPMHD实现使用无感近似也提出了导电和绝缘的边界，其中求解泊松方程来计算洛伦兹力，而不是演变的磁感应方程。这两种方法都对MHD基准进行了验证，包括自由表面MHD情况。所提出的无电感SPMHD实现具有稳定性和宽松的时间步长限制的优点，但仅在哈特曼数的低范围内是准确的。对于高哈特曼数问题，磁感应SPMHD模型更准确。对两种模型的计算效率和守恒误差进行了比较和讨论。
In order to solve incompressible, nonideal magnetohydrodynamic (MHD) free‐surface flows, two weakly compressible smoothed particle hydrodynamics models, with and without the consideration of magnetic induction, are developed. The SPH formulation for magnetic induction magnetohydrodynamics (SPMHD), which is popular in astrophysical studies, is applied for the first time to incompressible free‐surface MHD flows, such as liquid metal flows, with the consideration of nonideal MHD effects and boundaries with arbitrary electric conductivity. An SPMHD implementation using the inductionless approximation is also proposed for both electrically conductive and insulating boundaries, in which a Poisson equation is solved to compute the Lorentz force instead of evolving the magnetic induction equation. Both proposed methods are validated against MHD benchmarks, including free‐surface MHD cases. The proposed inductionless SPMHD implementation has the advantages of stability and relaxed time‐step restrictions, but is only accurate at a low range of Hartmann numbers. For high Hartmann number problems, magnetic induction SPMHD model is more accurate. The computational efficiency and conservation error of the two models are compared and discussed.