Technologies for supporting high-order geodesic mesh frameworks for computational astrophysics and space sciences

IF 16.281
Vladimir Florinski, Dinshaw S. Balsara, Sudip Garain, Katharine F. Gurski
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引用次数: 3

Abstract

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.

Abstract Image

支持用于计算天体物理学和空间科学的高阶测地线网格框架的技术
天体物理学、空间物理学和地球物理学中的许多重要问题都涉及球形物体(如恒星或行星)附近(可能是电离的)气体的流动。这种系统的几何形状自然有利于基于球面网格的数值方案。尽管极(经纬度)网格具有正交性,但由于极轴上的奇异性,导致区域大小的高度不均匀分布,因此不适合计算。后果是(a)?由于区域宽高比的大变化导致精度损失,以及(b)?由于时间步进的限制,计算效率较低。以柏拉图立体为模板的中心投影为基础的测地线网格解决了各向异性问题,但增加了生成的计算机代码的复杂性。本文描述了欧拉和MHD方程组在三角形测地线网格(TGM)上的一种新的有限体积实现,该实现在空间和时间上的精度可达四阶,并保留了磁场发散到机器精度。本文详细讨论了TGM的生成、区域分解技术、三维保守重构和时间步进技术。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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期刊介绍: Computational Astrophysics and Cosmology (CompAC) is now closed and no longer accepting submissions. However, we would like to assure you that Springer will maintain an archive of all articles published in CompAC, ensuring their accessibility through SpringerLink's comprehensive search functionality.
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