Stochastic modeling in fluid mechanics: data-based subgridscale models
The DFG SPP 1276 "MetStröm" covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of our part of this interdisciplinary research programm is the development and analysis of new data-based stochastic models for describing the low-scale phenomena in turbulent flows and meteorological data observations. Hence, new methods for clustering time series, that allow a simultaneous dimension reduction of the observed multiscale phenomena and a hidden state identification have to be evolved. Here, a cutting-edge PDE-approach involving FEM-based clustering algorithms, represents a promissing technique, that delivers the desired features and will be implemented and analysed in future research.