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

Authors
  • Florinski, Vladimir1
  • Balsara, Dinshaw S.2
  • Garain, Sudip2, 3
  • Gurski, Katharine F.4
  • 1 University of Alabama in Huntsville, Huntsville, USA , Huntsville (United States)
  • 2 University of Notre Dame, Notre Dame, USA , Notre Dame (United States)
  • 3 Korea Astronomy and Space Science Institute, Daejeon, Republic of Korea , Daejeon (South Korea)
  • 4 Howard University, Washington, USA , Washington (United States)
Type
Published Article
Journal
Computational Astrophysics and Cosmology
Publisher
Springer (Biomed Central Ltd.)
Publication Date
Mar 27, 2020
Volume
7
Issue
1
Identifiers
DOI: 10.1186/s40668-020-00033-7
Source
Springer Nature
Keywords
License
Green

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.

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