Hermitian approximation of the spherical divergence on the Cubed-Sphere

• Jean-Pierre Croisille ^[1]
  1. [1] University of Lorraine

     University of Lorraine

     Arrondissement de Nancy, Francia

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 280, Nº 1 (15 May 2015), 2015, págs. 188-201
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.11.047
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• Resumen

  • Previous work (Croisille, 2013) showed that the Cubed-Sphere grid offers a suitable discrete framework for extending Hermitian compact operators (Collatz, 1960) to the spherical setup. In this paper we further investigate the design of high-order accurate approximations of spherical differential operators on the Cubed-Sphere with an emphasis on the spherical divergence of a tangent vector field. The basic principle of this approximation relies on evaluating pointwise Hermitian derivatives along a series of great circles covering the sphere. Several test-cases demonstrate the very good accuracy of the approximate spherical divergence calculated with the new scheme.