Spherical Grid Creation and Modeling Using the Galerkin Compiler GC_Sphere

Abstract

The construction of spherical grids is, to a large extent, a question of organized programming. Such grids come in the form of rhomboidal/triangular grids and hexagonal grids. We are here mainly interested in Local-Galerkin high-order schemes and consider the classical fourth-order o4 method for comparison. High-order Local-Galerkin schemes imply sparse grids in a natural way, with an expected saving of computer runtime. Sparse grids on the sphere are described for rhomboidal and hexagonal cells. They are obtained by not using some of the full grid points. Technical problems and grid organization will be discussed with the purpose of reaching fully realistic applications. We present the description of a programming concept allowing people, using different programming styles at different locations, to work together. The concept of geometric files is introduced. Such geometric files can be offered for downloading and are supposed to allow Local-Galerkin methods to be introduced into an existing model with little effort. When the geometric files are known, the solution on a spherical grid is equivalent to the limited-area Galerkin solutions on the (irregular) plane grids on the patches. The proposed grids can be used with spectral elements (SE) and the Local-Galerkin methods o2o3 and o3o3. The latter offer an increased numerical efficiency which, in a toy model test, resulted in a ten-times-reduced computer run time.