Cluster-based reduced-order modelling (CROM) builds on the pioneering works of Gunzburger's group in cluster analysis [1] and Eckhardt's group in transition matrix models [2] and constitutes a potential alternative to reduced-order models based on a proper-orthogonal decomposition (POD). This strategy frames a time-resolved sequence of flow snapshots into a Markov model for the probabilities of cluster transitions. The information content of the Markov model is assessed with a Kullback-Leibler entropy. This entropy clearly discriminates between prediction times in which the initial conditions can be inferred by backward integration and the predictability horizon after which all information about the initial condition is lost. This approach is exemplified for a class of fluid dynamical benchmark problems like the periodic cylinder wake, the spatially evolving incompressible mixing layer, the bi-modal bluff body wake, and turbulent jet noise. For these examples, CROM is shown to distil nontrivial quasi-attractors and transition processes. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, and for the identification of precursors to desirable and undesirable events.
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5 December 2014
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 33rd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2013)
15–20 December 2013
Canberra, ACT, Australia
Research Article|
December 05 2014
Cluster-based reduced-order modelling of shear flows
Eurika Kaiser;
Eurika Kaiser
Institute PPRIME, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43, rue de l'Aérodrome, F-86036 Poitiers Cedex,
France
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Bernd R. Noack;
Bernd R. Noack
Institute PPRIME, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43, rue de l'Aérodrome, F-86036 Poitiers Cedex,
France
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Laurent Cordier;
Laurent Cordier
Institute PPRIME, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43, rue de l'Aérodrome, F-86036 Poitiers Cedex,
France
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Andreas Spohn;
Andreas Spohn
Institute PPRIME, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43, rue de l'Aérodrome, F-86036 Poitiers Cedex,
France
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Marc Segond;
Marc Segond
Ambrosys GmbH, Albert Einstein Str. 1-5, D-14469 Potsdam,
Germany
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Markus Abel;
Markus Abel
Ambrosys GmbH, Albert Einstein Str. 1-5, D-14469 Potsdam, Germany and Potsdam University, Institute for Physics and Astrophysics, Karl-Liebknecht Str. 24-25, D-14476 Potsdam,
Germany
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Guillaume Daviller;
Guillaume Daviller
CERFACS, 42 Avenue Gaspard Coriolis, F-31057 Toulouse Cedex 01,
France
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Marek Morzyński;
Marek Morzyński
Institute of Combustion, Engines and Transportation, Poznań University of Technology, PL 60-965 Poznań,
Poland
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Jan Östh;
Jan Östh
Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology, SE-412 96 Göteborg,
Sweden
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Siniša Krajnović;
Siniša Krajnović
Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology, SE-412 96 Göteborg,
Sweden
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Robert K. Niven
Robert K. Niven
School of Engineering and Information Technology, The University of New South Wales at Canberra, Australian Capital Territory, 2600, Australia and Institute PPRIME, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, T,
France
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AIP Conf. Proc. 1636, 151–158 (2014)
Citation
Eurika Kaiser, Bernd R. Noack, Laurent Cordier, Andreas Spohn, Marc Segond, Markus Abel, Guillaume Daviller, Marek Morzyński, Jan Östh, Siniša Krajnović, Robert K. Niven; Cluster-based reduced-order modelling of shear flows. AIP Conf. Proc. 5 December 2014; 1636 (1): 151–158. https://doi.org/10.1063/1.4903725
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