A fully spectral methodology for magnetohydrodynamic calculations in a whole sphere
A fully spectral methodology for magnetohydrodynamic calculations in a whole sphere
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DOI：
10.1016/j.jcp.2015.10.056
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发表时间：
2016-01
期刊：
影响因子：
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通讯作者：
P. Marti;A. Jackson
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文献类型：
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作者：
P. Marti;A. Jackson
本文提出了一种全谱方法用于全球磁流体动力学（MHD）计算。使用琼斯-沃兰多项式的径向扩展保证了物理变量在整个球形体积中保持无限可微。此外，我们提出了一个数学上的动机和系统的策略，放松非常严格的时间步长的约束，是目前接近原点时，球谐展开用于角方向。新的约束允许显着的节省，即使在相对简单的解决方案上所示的所谓的全球基准，一个特定的问题，一个非常准确的解决方案。数值实现使用2D数据分解，这允许它在当今的高性能计算系统上扩展到数千个核心。除了验证结果，我们还提出了三个新的全球发电机解决方案，提出了一个相对简单的结构。
We present a fully spectral methodology for magnetohydrodynamic (MHD) calculations in a whole sphere. The use of Jones–Worland polynomials for the radial expansion guarantees that the physical variables remain infinitely differentiable throughout the spherical volume. Furthermore, we present a mathematically motivated and systematic strategy to relax the very stringent time step constraint that is present close to the origin when a spherical harmonic expansion is used for the angular direction. The new constraint allows for significant savings even on relatively simple solutions as demonstrated on the so-called full sphere benchmark, a specific problem with a very accurately-known solution. The numerical implementation uses a 2D data decomposition which allows it to scale to thousands of cores on present-day high performance computing systems. In addition to validation results, we also present three new whole sphere dynamo solutions that present a relatively simple structure.