TY - GEN
A1 - Kaiser, Eurika
A1 - Noack, Bernd R.
A1 - Cordier, Laurent
A1 - Spohn, Andreas
A1 - Segond, Marc
A1 - Abel, Markus
A1 - Daviller, Guillaume
A1 - Osth, Jan
A1 - Krajnovic, Sinisa
A1 - Niven, Robert K.
T1 - Cluster-based reduced-order modelling of a mixing layer
T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 605
KW - low-dimensional models
KW - nonlinear dynamical systems
KW - shear layers
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-416113
SN - 1866-8372
IS - 605
SP - 365
EP - 414
ER -