支持计算天体物理学和空间科学高阶测地线网格框架的技术
Technologies for supporting high-order geodesic mesh frameworks for computational astrophysics and space sciences
摘要：
天体物理学、空间物理学和天体物理学中的许多重要问题都涉及到球形物体（如恒星或行星）附近的（可能是电离的）气体流动。这种系统的几何形状自然有利于基于球形网格的数值方案。尽管其正交性，极（纬度-经度）网格是不适合计算，因为极轴上的奇异性，导致区域大小的高度不均匀分布。结果是（a）由于区域纵横比的大变化而损失精度，以及（b）由于时间步进的严重限制而导致计算效率差。基于中心投影的测地线网格使用柏拉图立体作为模板，解决了各向异性问题，但增加了所得计算机代码的复杂性。我们描述了一个新的有限体积实现的欧拉和MHD方程组的三角形测地线网格（TGM），是准确的四阶空间和时间，并保存的磁场的发散机器精度。本文详细讨论了TGM的生成，区域分解技术，三维保守重建和时间步进。
英文摘要：
Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical schemes based on a spherical mesh. Despite its orthogonality property, the polar (latitude-longitude) mesh is ill suited for computation because of the singularity on the polar axis, leading to a highly non-uniform distribution of zone sizes. The consequences are (a) loss of accuracy due to large variations in zone aspect ratios, and (b) poor computational efficiency from a severe limitations on the time stepping. Geodesic meshes, based on a central projection using a Platonic solid as a template, solve the anisotropy problem, but increase the complexity of the resulting computer code. We describe a new finite volume implementation of Euler and MHD systems of equations on a triangular geodesic mesh (TGM) that is accurate up to fourth order in space and time and conserves the divergence of magnetic field to machine precision. The paper discusses in detail the generation of a TGM, the domain decomposition techniques, three-dimensional conservative reconstruction, and time stepping.
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