‘The Equator–Pole grid system’: an overset grid system for the sphere, with an optimal uniformity property

Abstract

This article proposes a new grid system for the sphere, which consists of three orthogonal and almost uniform grids. The basic one is a latitude-longitude grid covering an annular band around the equator. For the rest of the sphere this grid is complemented by two grids covering the polar regions, and based on suitably modified stereographic coordinates. The rectangular structure of the grids makes highly efficient implementation on massively parallel computer systems possible. Numerical experiments with the new grid system are carried out for two advection examples, namely smooth deformational flow and rotation of the Cosine bell, and for the test problems 2, 3, and 6 from Williamson et al., concerning the non-linear shallow water equations. For problem 6, the Rossby–Haurwitz wave, we study conservation properties for mass and energy. The computational results compare favourably with results for other grids. Our focus is the definition of the grid system together with the connection between grids by overlapping and the use of centred interpolation formulas. The method of centred finite differences is used for the spatial discretisation of the differential equations, because it is well-known and easy to implement.

Keywords

• spherical overset grid system
• optimal uniformity
• strict overlapping
• shallow water equations
• AMS Subject Classification: 35L45
• 65M06