Space-Filling Curves for 2.5-Dimensional Meshes

Abstract

Many physical processes of the Earths atmosphere like cloud processes, convection or radiation, are strongly coupled vertically. The numerical solution of these processes motivates a higher resolution in vertical z-direction than in horizontal x- and y-direction in adaptive mesh refinement. This anisotropic mesh refinement is represented as the Cartesian product of a horizontal 2-dimensional isotropic refinement and a vertical 1-dimensional isotropic refinement. The vertical refinement depends on the horizontal refinement and hence the term 2.5-dimensional mesh refinement is introduced. It refers to the anisotropic adaptive mesh refinement for hexahedra and prisms. A space-filling curve is used to store the elements resulting from adaptive mesh refinement. In this thesis, a space-filling curve for 2.5 dimensional adaptive mesh refinement is developed. The 2.5-dimensional space-filling curve is used to implement anisotropic 2.5-dimensional adaptive mesh refinement in the already existing isotropic tree-based approach for adaptive mesh refinement in the open-source library t8code.