The spiral grid: A new approach to discretize the sphere and its application to mantle convection

Abstract

This paper presents a new method to generate a three-dimensional spherical grid using natural neighbor Voronoi cells distributed by spiral functions. A unique property of this grid is the complete removal of symmetries with arbitrary selectable lateral and radial resolution, which are not restricted to discrete radial levels or geometrical constraints as compared to the commonly used grids based on projected triangulated platonic solids such as a cube, a rhomboid, or an icosahedron. The spiral grid can be refined in certain areas of interest and makes it possible to have a very small inner radius to outer radius ratio. Cell volumes can be made almost constant throughout the computational domain. Analysis, statistics, and computation methods are described in detail, as well as a possible domain decomposition suitable for parallel computing. Conductive temperature profiles were numerically calculated in the spherical shell and directly compared with the analytic solution as verification. The grid is applied to numerical simulations of mantle convection using a finite volume scheme. The model is validated by a comparison of steady state cubic and tetrahedral convection patterns with other published models.