Adaptive Gittergenerierung für das Finite-Elemente-Ozean- und Meereismodell FESOM

Abstract

To circumvent the problems which arise at the discretizing stage of ocean general circulation models (OGCM) with the Finite Difference Method and to improve the local conservation properties, the three dimensional Finite Element Sea Ice-Ocean Model (FESOM) was already developed at the Alfred-Wegener-Institut - Helmholtz-Zentrum für Polar- und Meeresforschung (AWI), Bremerhaven. The model discretization of FESOM was done with the Finite Element Method and the underlying three-dimensional mesh consists of an unstructured surface mesh and a structured tetrahedra mesh. In this thesis the mesh generator Meshgen4FESOM (with additional supporting tools) will be presented, which generates iteratively and automatically a FESOM mesh of the above structure. The surface mesh will be generated in an adaptive fashion using local element errors (which are calculated on the basis of the elements local bathymetry) and the corresponding global error in every iteration. Additionally different mesh smoothing techniques will be applied to the surface mesh. The tetrahedra mesh will be constructed iteratively by continuing the triangle elements of the surface mesh to the ocean bottom which yields a prism for every surface element. After that, every prism will be subdivided into smaller prisms at predefined levels and finally every subprism is cut into three tetrahedra. In a last step a remeshing of the tetrahedra in every level will be done, to get an optimal triangulation with respect to the bathymetry and in accordance to the needs of FESOM. It is the main goal of this thesis to develop meshing techniques and create a meshgenerator which constructs a family of surface and tetrahedrameshes which takes account of the bathymetry in an adaptive way, to resolve coasts, straits and other dynamical regions of the oceans and leaves non dynamical bathymetry regions more coarse.