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SPP 1276:  Multiple Scales in Fluid Mechanics and Meteorology

Subject Area Thermal Engineering/Process Engineering
Geosciences
Mathematics
Physics
Term from 2007 to 2016
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 25965762
 
The reliable simulation of local extremes, such as precipitating fronts with high flood risk (meteorology) or local extreme temperatures in combustion chambers (fluid mechanics), is both of high practical importance and one of the major challenges in these research fields: How can we, e.g., simulate the 10-50 km sized "eye" of a hurricane together with the storm's determining large-scale environment at high fidelity without exhausting the available computing resources? One approach to this challenge relies on spatio-temporal grid-size adaptation controlled by both the pertaining flow conditions and by the questions the simulation is meant to answer. If, e.g., we are interested in the actual size, position and strength of the "eye" of a hurricane, then grid sizes of about 1 km should be sufficient; if we intend to simulate individual updraughts inside such a storm, then mesh widths of 100 m are more appropriate; if some range of turbulent fluctuations is to be represented as well, the mesh size must be even smaller; etc., all the way down to the micrometer-sized droplets within a cloud.
How should one, on a time-dependent grid that dynamically adapts to the flow state and to the simulation's targeted question, account for the fact that any change of the spatio-temporal grid size will shift the boundary between those processes that can and those that cannot be resolved on the computational mesh? What kind of combination of (scale-dependent) mathematical models and adaptive numerical schemes is suited to satisfy the standards of meteorology and fluid dynamics with respect to the reliability of a simulation as well as the standards of mathematics as far as well-posedness of the overall mathematical problem is concerned?
These are the key questions, which researchers from meteorology, fluid dynamics and mathematics address in bi- and tri-disciplinary projects within the Priority Programme. The projects aim at providing simulation models in which scale-dependent descriptions of physical processes, their mathematical formulation and the adaptive discretisations used to translate them to computer-tractable problems interleave consistently. For the representation of processes not resolved on the computational mesh, deterministic continuum-type models are considered as well as discrete and stochastic closure schemes. Besides the development of fundamental concepts and their prototypical implementation, novel error estimators are being developed, which allow the separate estimation of numerical and modelling errors, and which provide the basis for the dynamical control of grid and model adaptation. The theoretical projects are complemented by judiciously chosen experimental investigations providing reference data for simulation validation.
DFG Programme Priority Programmes
International Connection Austria, Switzerland, United Kingdom, USA

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