Hermitian approximation of the spherical divergence on the Cubed-Sphere

Jean-Pierre Croisille (1)

1 IECL - Institut Élie Cartan de Lorraine

Previous work [7] showed that the Cubed-Sphere grid offers a suitable discrete framework for extending Hermitian compact operators [6] 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.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Jean-Pierre Croisille. Hermitian approximation of the spherical divergence on the Cubed-Sphere. Journal of Computational and Applied Mathematics, 2015, 280, pp.188-201. ⟨10.1016/j.cam.2014.11.047⟩. ⟨hal-01283649⟩