Abstract
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.
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