Application of the terrain-following coordinates to discontinuous Galerkin schemes

Kurzfassung

This thesis deals with the discontinuous Galerkin method using terrain-following coordinates and was written under the supervision of the Institute of Software Technology of the German Aerospace Center (DLR). In this thesis, the theoretical and the discrete DG formulation are explained. The coordinate transformation between the terrain-following and Cartesian coordinates is introduced by using tensor algebra and tensor analysis. Furthermore, the derivation of a DG formulation in the terrain-following system with metric terms and Cartesian parameters is formulated. The aim of this thesis is to create and validate a prototype of a julia library that provides the grids and transformation terms for transformations between Cartesian and terrainfollowing coordinates with one- and two-dimensional orographys