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**Harvard**

Kaiser, E., Noack, B., Cordier, L., Spohn, A., Segond, M., Abel, M., Daviller, G., Östh, J., Krajnovic, S. och Niven, R. (2014) *Cluster-based reduced-order modelling of a mixing layer*.

** BibTeX **

@article{

Kaiser2014,

author={Kaiser, Eurika and Noack, Bernd R. and Cordier, Laurent and Spohn, Andreas and Segond, Marc and Abel, Marcus and Daviller, Guillaume and Östh, Jan and Krajnovic, Sinisa and Niven, Robert K.},

title={Cluster-based reduced-order modelling of a mixing layer},

journal={Journal of Fluid Mechanics},

issn={0022-1120},

volume={754},

pages={ 365-414},

abstract={We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger’s group (Burkardt, Gunzburger & Lee, Comput. Meth. Appl. Mech. Engng, vol. 196, 2006a, pp. 337–355) and transition matrix models introduced in fluid dynamics in Eckhardt’s group (Schneider, Eckhardt & Vollmer, Phys. Rev. E, vol. 75, 2007, art. 066313). CROM constitutes a potential alternative to POD models and generalises the Ulam–Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron–Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Second, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent (FTLE) and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.},

year={2014},

keywords={ low-dimensional models, nonlinear dynamical systems,shear layers},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 201156

A1 Kaiser, Eurika

A1 Noack, Bernd R.

A1 Cordier, Laurent

A1 Spohn, Andreas

A1 Segond, Marc

A1 Abel, Marcus

A1 Daviller, Guillaume

A1 Östh, Jan

A1 Krajnovic, Sinisa

A1 Niven, Robert K.

T1 Cluster-based reduced-order modelling of a mixing layer

YR 2014

JF Journal of Fluid Mechanics

SN 0022-1120

VO 754

SP 365

OP 414

AB We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger’s group (Burkardt, Gunzburger & Lee, Comput. Meth. Appl. Mech. Engng, vol. 196, 2006a, pp. 337–355) and transition matrix models introduced in fluid dynamics in Eckhardt’s group (Schneider, Eckhardt & Vollmer, Phys. Rev. E, vol. 75, 2007, art. 066313). CROM constitutes a potential alternative to POD models and generalises the Ulam–Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron–Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Second, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent (FTLE) and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.

LA eng

DO 10.1017/jfm.2014.355

LK http://dx.doi.org/10.1017/jfm.2014.355

OL 30