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首页> 外文期刊>Journal of Computational Physics >Induced electric current-based formulation in computations of low magnetic Reynolds number magnetohydrodynamic flows
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Induced electric current-based formulation in computations of low magnetic Reynolds number magnetohydrodynamic flows

机译：低磁雷诺数磁流体动流计算中基于感应电流的公式

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摘要

We use the induced electric current as the main electromagnetic variable to compute low magnetic Reynolds number magnetohydrodynamic (MHD) flows. The equation for the induced electric current is derived by taking the curl of the induction equation and using Ampère's law. Boundary conditions on the induced electric current are derived at the interface between the liquid and the thin conducting wall by considering the current loop closing in the wall and the adjacent liquid. These boundary conditions at the liquid-solid interface include the Robin boundary condition for the wall-normal component of the current and an additional equation for the wall potential to compute the tangential current component. The suggested formulation (denominated j-formulation) is applied to three common types of MHD wall-bounded flows by implementing the finite-difference technique: (i) high Hartmann number fully developed flows in a rectangular duct with conducting walls; (ii) quasi-two-dimensional duct flow in the entry into a magnet; and (iii) flow past a magnetic obstacle. Comparisons have been performed against the traditional formulation based on the induced magnetic field (B-formulation), demonstrating very good agreement.
机译：我们使用感应电流作为主要电磁变量来计算低磁雷诺数磁流体动力学（MHD）流量。感应电流的方程式是通过将感应方程式的卷度和安培定律推导出来的。通过考虑壁和相邻液体中的电流环路闭合，可以在液体和薄导电壁之间的界面上导出感应电流的边界条件。液-固界面处的这些边界条件包括电流壁法向分量的Robin边界条件和壁电势的附加方程，以计算切向电流分量。通过实施有限差分技术，将建议的公式（以j公式表示）应用于三种常见的MHD壁边界流动：（i）在具有导电壁的矩形管道中充分发展的高Hartmann数流; （ii）进入磁体的准二维管道流; （iii）流过磁性障碍物。已基于感应磁场（B配方）与传统配方进行了比较，证明了很好的一致性。

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