The selection and adaptation of numerical methods for modeling of atmospheric processes is of great importance considering the growing complexity of the models. Such methods need to be evaluated according to their precision and conservation of physical properties together with the need for high efficiency on different computer systems. In particular, parallelizing algorithms is often necessary to make them applicable to specific problems.
Time Integration Techniques. The description of atmospheric processes generally leads to systems of stiff differential equations. For such systems explicit integration methods are only stable for very small time steps. For this purpose implicit-explicit (IMEX) methods were developed. The most important components of these IMEX methods are suitable algorithms for large systems of linear equations that make use of the special sparse structures of the problems. A further gain in efficiency is obtained by so-called multi-rate procedures, which allow the use of different time step sizes in separate model regions and for different processes.
Numerics of Weather Forecasts. Within the DFG research program MetStroem the use of Cartesian grids for computing atmospheric flows is investigated. Such grids promise an improved representation of the stable atmosphere as well as improved precipitation forecasts in structured terrains. Block adaptive grids are used to obtain constant vertical resolutions. For this grid structure, adapted space- and time discretisations are developed and tested within the flow model ASAM.
Model Coupling and Parallelization. In many cases numerical models are only representing special parts of a complex system. Coupling such models allows the representation of the interactions between different parts of the systems. At the IfT the chemistry-transport code MUSCAT was coupled with the regional weather forecast model LM of the DWD (German weather service). For this purpose different strategies for online-coupling and load balancing were investigated. The coupling schemes have to ensure a great flexibility together with considering feedbacks between models.
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