A fully spectral methodology for magnetohydrodynamic calculations in a whole sphere

JOURNAL OF COMPUTATIONAL PHYSICS

卷:305

Article

Marti, P.^1,2  Jackson, A.² 

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[2] ETH, Inst Geophys, CH-8092 Zurich, Switzerland

关键词: Sphere;    CFL condition;    HPC;    Spectral method;    Dynamo;    Orthogonal poylnomials;    MHD;   

DOI  :  10.1016/j.jcp.2015.10.056

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free