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Variational multiscale based data driven modeling of subgrid scales for fluid mechanics applications

Variational multiscale based data driven modeling of subgrid scales for fluid mechanics applications

Field of influence of the fine scales for a classical method (left) and a discontinuous Galerkin method (right).
Field of influence of the fine scales for a classical method (left) and a discontinuous Galerkin method (right).
Leaders:  Dominik Schillinger
Team:  Stein Stoter
Year:  2020
Sponsors:  Deutsche Forschungsgemeinschaft (DFG) via the Emmy Noether Award SCH 1249/2-1

In recent work, we have cast various non-standard finite element formulations for advection based PDEs in the variational multiscale framework. Examples are Nitsche’s formulation and discontinuous Galerkin methods. This formalism has revealed the implicit multiscale decomposition inherent to these methods.

Now, we extend upon this formalism and aim to develop localization techniques for the remaining fine scale interaction. Even after localization, determining the true scale interaction remains computationally expensive. During an offline stage, we produce training data of precise scale interaction for ranges of element shapes and underlying advective fields. A trained machine learning algorithm is used during the online phase to approximate the interaction with the unresolved scales, i.e., the turbulent subgrid scales. Our goal is thus to develop a highly capable, data driven, turbulence modeling tool with a mathematically rigorously foundation.