FROYLAND, GARY GONZÁLEZ-TOKMAN, CECILIA and MURRAY, RUA 2018. Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, p. 1.
Kaiser, Eurika Morzyński, Marek Daviller, Guillaume Kutz, J. Nathan Brunton, Bingni W. and Brunton, Steven L. 2018. Sparsity enabled cluster reduced-order models for control. Journal of Computational Physics, Vol. 352, p. 388.
Xie, Xuping Wells, David Wang, Zhu and Iliescu, Traian 2018. Numerical analysis of the Leray reduced order model. Journal of Computational and Applied Mathematics, Vol. 328, p. 12.
Loiseau, Jean-Christophe and Brunton, Steven L. 2018. Constrained sparse Galerkin regression. Journal of Fluid Mechanics, Vol. 838, p. 42.
Taira, Kunihiko Brunton, Steven L. Dawson, Scott T. M. Rowley, Clarence W. Colonius, Tim McKeon, Beverley J. Schmidt, Oliver T. Gordeyev, Stanislav Theofilis, Vassilios and Ukeiley, Lawrence S. 2017. Modal Analysis of Fluid Flows: An Overview. AIAA Journal, Vol. 55, Issue. 12, p. 4013.
Varon, Eliott Eulalie, Yoann Edwige, Stephie Gilotte, Philippe and Aider, Jean-Luc 2017. Chaotic dynamics of large-scale structures in a turbulent wake. Physical Review Fluids, Vol. 2, Issue. 3,
Kushwaha, Anubhav Park, Jae Sung and Graham, Michael D. 2017. Temporal and spatial intermittencies within channel flow turbulence near transition. Physical Review Fluids, Vol. 2, Issue. 2,
Ştefănescu, Răzvan and Sandu, Adrian 2017. Efficient approximation of Sparse Jacobians for time-implicit reduced order models. International Journal for Numerical Methods in Fluids, Vol. 83, Issue. 2, p. 175.
Manohar, Krithika Brunton, Steven L. and Kutz, J. Nathan 2017. Environment identification in flight using sparse approximation of wing strain. Journal of Fluids and Structures, Vol. 70, p. 162.
Wei, Zheng Yang, Zhigang Xia, Chao and Li, Qiliang 2017. Cluster-based reduced-order modelling of the wake stabilization mechanism behind a twisted cylinder. Journal of Wind Engineering and Industrial Aerodynamics, Vol. 171, p. 288.
Kaiser, Eurika Noack, Bernd R. Spohn, Andreas Cattafesta, Louis N. and Morzyński, Marek 2017. Cluster-based control of a separating flow over a smoothly contoured ramp. Theoretical and Computational Fluid Dynamics, Vol. 31, Issue. 5-6, p. 579.
Brunton, Steven L. Brunton, Bingni W. Proctor, Joshua L. Kaiser, Eurika and Kutz, J. Nathan 2017. Chaos as an intermittently forced linear system. Nature Communications, Vol. 8, Issue. 1,
Noack, Bernd R. 2016. From snapshots to modal expansions – bridging low residuals and pure frequencies. Journal of Fluid Mechanics, Vol. 802, p. 1.
Taira, Kunihiko Nair, Aditya G. and Brunton, Steven L. 2016. Network structure of two-dimensional decaying isotropic turbulence. Journal of Fluid Mechanics, Vol. 795,
Guéniat, Florimond Mathelin, Lionel and Hussaini, M. Yousuff 2016. A statistical learning strategy for closed-loop control of fluid flows. Theoretical and Computational Fluid Dynamics, Vol. 30, Issue. 6, p. 497.
Bright, Ido Lin, Guang and Kutz, J. Nathan 2016. Classification of Spatiotemporal Data via Asynchronous Sparse Sampling: Application to Flow around a Cylinder. Multiscale Modeling & Simulation, Vol. 14, Issue. 2, p. 823.
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.
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