Showing papers on "Dynamic mode decomposition published in 2010"

Dynamic mode decomposition of numerical and experimental data

Abstract: The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders.

Reduced-order models for flow control: balanced models and Koopman modes

Abstract: This paper addresses recent developments in model-reduction techniques applicable to fluid flows. The main goal is to obtain low-order models tractable enough to be used for analysis and design of feedback laws for flow control, while retaining the essential physics. We first give a brief overview of several model reduction techniques, including Proper Orthogonal Decomposition [3], balanced truncation [8, 9], and the related Eigensystem Realization Algorithm [5, 6], and discuss strengths and weaknesses of each approach. We then describe a new method for analyzing nonlinear flows based on spectral analysis of the Koopman operator, a linear operator defined for any nonlinear dynamical system. We show that, for an example of a jet in crossflow, the resulting Koopman modes decouple the dynamics at different timescales more effectively than POD modes, and capture the relevant frequencies more accurately than linear stability analysis.