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Treatment of the magnetic field for geodynamo simulations using the finite element method

机译：使用有限元方法处理地球动力学模拟的磁场

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摘要

We propose a scheme for calculating the magnetic field in a spherical shell, based on Earth's outer core, using the finite element method (FEM). The two most difficult problems for magnetohydrodynamics (MHD) simulations in a rotating spherical shell with FEM are solving the magnetic field outside the fluid shell, and connecting the magnetic field in the fluid shell to the exterior potential field at the boundary. To solve these problems, we extend the finite element mesh beyond the fluid shell and compute the vector potential of the magnetic field. To verify the present scheme, we consider three test case. First, we compare the FEM model with an analytical solution of Laplace's equation outside the fluid. Second, we evaluate free decay of a dipole field and compare the results with a spectral solution. Finally, compare the results of a simple kinematic dynamo problem with a spectral solution. The results suggest that the accuracy of the dipole field depends on the radius of the simulation domain, and that this error becomes sufficiently small if the radius of the outer region is approximately 6 times larger than the radius of the fluid shell.
机译：我们提出了一种基于地球外核的球壳磁场计算方法，该方法使用有限元方法（FEM）。在具有FEM的旋转球形壳体中进行磁流体动力学（MHD）模拟的两个最困难的问题是求解流体壳体外部的磁场，并将流体壳体中的磁场连接到边界处的外部势场。为了解决这些问题，我们将有限元网格扩展到流体壳之外，并计算磁场的矢量势。为了验证本方案，我们考虑三个测试案例。首先，我们将FEM模型与流体外部Laplace方程的解析解进行比较。其次，我们评估偶极子场的自由衰减并将结果与​​频谱解决方案进行比较。最后，将简单的运动发电机问题的结果与频谱解决方案进行比较。结果表明，偶极子场的精度取决于模拟域的半径，并且如果外部区域的半径大约是流体壳的半径的6倍，则该误差会变得足够小。

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