Adaptive Numerical Simulation of Idealized Cyclones
Seminar Room 1, Newton Institute
The processes causing a cyclone's formation, its intensification, its motion and finally its terminating all proceed at multiple and interacting temporal and spatial scales. Therefore the forecasting of a cyclone's dynamic can make great benefits of adaptive techniques such as local mesh refinement. Mesh adaptation strategies are often based on problem-dependent indicators that need to be determined and which have different properties with respect to the associated computational effort and the quality of the resulting meshes. For example, the computation of goal-oriented error indicators requires sensitivity information provided by the solution of an additional linear problem which leads to a remarkable overhead in computation time and additional storage requirements. In that context, we address the question whether the complexity of different criteria for refinement is justifiable. To this end, we investigate idealized cyclone scenarios and systematically analyze the efficiency of adaptive numerical methods employing a selection of different indicators based on physical criteria, heuristic criteria, a posteriori error estimators, and goal-oriented approaches. We compare these approaches with regard to the related computational costs, storage requirements, implementation complexity, and the accuracy of the resulting solution.