Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-37607 Wissenschaftlicher Artikel Kaiser, Eurika; Noack, Bernd R.; Cordier, Laurent; Spohn, Andreas; Segond, Marc; Abel, Markus; Daviller, Guillaume; Osth, Jan; Krajnovic, Sinisa; Niven, Robert K. Cluster-based reduced-order modelling of a mixing layer New York Cambridge Univ. Press 2014 50 Journal of fluid mechanics 754 365 414 10.1017/jfm.2014.355 Institut für Physik und Astronomie OPUS4-41611 misc Kaiser, Eurika; Noack, Bernd R.; Cordier, Laurent; Spohn, Andreas; Segond, Marc; Abel, Markus; Daviller, Guillaume; Osth, Jan; Krajnovic, Sinisa; Niven, Robert K. Cluster-based reduced-order modelling of a mixing layer 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. 2014 50 Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe 605 365 414 urn:nbn:de:kobv:517-opus4-416113 10.25932/publishup-41611 Mathematisch-Naturwissenschaftliche Fakultät