The group "Numerical Methods in Geosciences" develops methods for efficiently solving multi-scale geoscientific problems numerically. An unsolved question in such simulations is the correct description and numerical representation of multi-scale processes. These are for example, the influence of small-scale mixing and entrainment processes of moist air at cloud boundaries on the development of the entire cloud cluster, the interaction of long tsunami waves with highly complex topography, or the trigger of large-scale wave phenomena from small-scale perturbations (the butterfly effect). One of our key objectives is therefore the development of Adaptive Multi-Scale Methods.
In order to capture these effects, adaptive numerical methods are developed, which are capable of detecting areas needing high resolution on the fly, and adapting to these dynamical processes automatically. At the same time, small scale processes need to be represented in large scale simulations in a mathematically correct manner. The automatic adaptation as well as the numerical upscaling demand for highly accurate, robust, and structure-preserving numerical methods, which - applied to geophysical fluid dynamics problems - form the Numerical Methods for Geophysical Fluid Dynamics focus of the group’s work.
Furthermore, efficient implementation of these demanding methods on high-performance computers including large numbers of processors is a must and new techniques for achieving scalability and efficiency are being developed and are the objective of Efficient Algorithms for High Performance Computing developments.