Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Journal of Computational Physics
Semi-Implicit Spectral Element Atmospheric Model
Journal of Scientific Computing
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Fast Algorithms for Spherical Harmonic Expansions
SIAM Journal on Scientific Computing
A wave propagation method for hyperbolic systems on the sphere
Journal of Computational Physics
Finite-volume transport on various cubed-sphere grids
Journal of Computational Physics
Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme
Journal of Computational Physics
A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid
Journal of Computational Physics
Journal of Computational Physics
High-order finite-volume methods for the shallow-water equations on the sphere
Journal of Computational Physics
A class of deformational flow test cases for linear transport problems on the sphere
Journal of Computational Physics
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The cubed-sphere grid is a spherical grid made of six quasi-cartesian square-like patches. It was originally introduced in Sadourny (Mon Weather Rev 100:136---144, 1972). We extend to this grid the design of high-order finite-difference compact operators (Collatz, The numerical treatment of differential equations. Springer, Berlin, 1960; Lele, J Comput Phys 103:16---42, 1992). 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 specific 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. (J Comput Phys 102:211---224, 1992) and a deformational test-case reported in Nair and Lauritzen (J Comput Phys 229:8868---8887, 2010).