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首页> 外文期刊>International journal of non-linear mechanics >Numerical simulations of highly non-linear coupled full MHD equations in spherical geometry
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Numerical simulations of highly non-linear coupled full MHD equations in spherical geometry

机译：球形几何中高度非线性耦合的完整MHD方程的数值模拟

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Numerical simulations have been performed to solve highly non-linear coupled full MHD equations in spherical polar coordinates. The control of flow separation behind a sphere using Lorentz forces is investigated at moderate magnetic Reynolds numbers. An external magnetic field is applied in the direction of the steady, viscous and electrically conducting flow such that it is aligned at large distances from the sphere. The governing equations are coupled non-linear Navier-Stokes and non-linear Maxwell's equations. The parameters that governs the flow are Reynolds number Re, magnetic Reynolds number R_m and Alfven number β. The finite difference method combined with multigrid technique is used to solve the full MHD equations which are expressed in vorticity, stream function and magnetic stream function form. All the non-linearities in the momentum equation due to Lorentz force are handled effectively. It is found that the separation for highly conducting fluids can be suppressed with low magnetic fields. The drag coefficient is found to decrease for β ≤ 1 and then increase. The results agree with experimental results.
机译：已经进行了数值模拟，以解决球形极坐标中的高度非线性耦合的完整MHD方程。研究了在中等磁雷诺数下利用洛伦兹力控制球体后流分离的方法。沿稳定，粘性和导电流的方向施加外部磁场，以使其与球体相距很远。控制方程是耦合的非线性Navier-Stokes方程和非线性的Maxwell方程。控制流量的参数是雷诺数Re，雷诺磁数R_m和阿尔芬数β。结合多网格技术的有限差分法被用于求解完整的MHD方程，这些方程以涡度，流函数和磁流函数形式表示。动量方程中由于洛伦兹力引起的所有非线性均得到有效处理。发现使用低磁场可以抑制高导电流体的分离。发现阻力系数在β≤1时减小，然后增大。结果与实验结果吻合。

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