Hermitian Compact Interpolation on the Cubed-Sphere Grid

The cubed-sphere grid is a spherical grid made of six quasi-cartesian square-like patches. It was originally introduced in [21]. We extend to this grid the design of high-order nite-di erence compact operators [4, 11]. The present work is limitated to the design of a fourth-order accurate spherical gradient. The treatment at the interface of the six patches relies on a speci c interpolation system which is based on using great circles in an essential way. The main interest of the approach is a fully symmetric treatment of the sphere. We numerically demonstrate the accuracy of the approximate gradient on several test problems, including the cosine-bell test-case of Williamson et al. [27] and a deformational test-case reported in [13].