Repository: Freie Universit├Ąt Berlin, Math Department

Towards a Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation

von Larcher, T. and Beck, A. and Klein, R. and Horenko, I. and Metzner, Ph. and Waidmann, M. and Igdalov, D. and Gassner, G. and Munz , C.-D. (2015) Towards a Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation. Meteorologische Zeitschrift, 24 (3). pp. 313-342.

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Abstract

We focus on a mixed deterministic-stochastic subgrid scale modelling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Our concept is based on the integral conservation laws for mass, momentum and energy of a flow field. We model the space-time structure of the flux correction terms to create a discrete formulation. Advanced methods of time series analysis for the data-based construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory based on a modified Akaike information criterion and on the Bayesian information criterion for the model discrimination are used to construct surrogate models for the non-resolved flux fluctuations. Vector-valued auto-regressive models with external influences form the basis for the modelling approach. The reconstruction capabilities of the modelling ansatz are tested against fully 3D turbulent channel flow data computed by direct numerical simulation and, in addition, against a turbulent Taylor-Green vortex flow showing a transition from laminar to a turbulent flow state. The modelling approach for the LES closure is different in both test cases. In the channel flow we consider an implicit LES ansatz. In the Taylor-Green vortex flow, it follows an explicit closure approach. We present here the outcome of our reconstruction tests and show specific results of the non-trivial time series data analysis. Started with a generally stochastic ansatz we found, surprisingly, that the deterministic model part already yields small residuals and is, therefore, good enough to fit the flux correction terms well. In the Taylor-Green vortex flow, we found additionally time-dependent features confirming that our modelling approach is capable of detecting changes in the temporal structure of the flow. The results encourage us to launch a more ambitious attempt at dynamic LES closure along these lines.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:1373
Deposited By: Ulrike Eickers
Deposited On:28 Jan 2014 08:14
Last Modified:29 Jan 2016 09:22

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