An Adaptive Shallow Water Model on the Sphere

Abstract

This thesis describes the adaptive shallow water model PLASMA-FEMmE. It solves on the sphere the shallow water equations, the prototype for partial differential equations in atmospheric modeling, using a semi-implicit semi-Lagrangian time step and linear finite elements. Both statically and dynamically adapted grids created by the grid generator amatos are investigated. The results are compared with those of the predecessor model FEMmE that uses a static uniform grid.The outcome demonstrates the capability of the chosen approach as well as its limits. Grid adaptation can easily be achieved with amatos. No reflexions at the grid interfaces are observed. Though in one test case instabilities are released at the grid interfaces. The numerical errors are reduced without a considerable enhancement of the computational effort in another test case with a well-known analytical solution. In respect to the conservation properties the results are more complicated. Mass conservation can be achieved in one test case with an appropriate static grid. In case of complex flow regimes all conservation properties are weakened duringthe simulation using dynamic grid adaptation.Nevertheless it can be concluded that the investigated scheme works out fine within the expectations. There is additional research effort to get a deeper understanding of the interactions between the involved physical processes and the numerical schemes. Together with that understanding and conservative advection schemes as well as more sophisticated adaption criteria there is hope that the aforementioned problems can be overcome.