Dynamic mode decomposition of numerical and experimental data

Abstract

International audienceThe 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. © 2010 Cambridge University Press

Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

“…The benefit of using these functions is that their spatial derivatives are known and numerically efficient algorithms such as the Fast Fourier Transform (FFT) can be utilized. In the context of MOR, the spatial basis functions can be derived a priori using completeness conditions (Ladyzhenskaia et al 1969;Noack & Eckelmann 1994), from Navier-Stokes eigenfunctions (Joseph 1976), or a posteriori from a snapshot of a solution data set, like the Proper Orthogonal Decomposition (POD) (Holmes et al 2012) or Dynamic Mode Decomposition (DMD) (Rowley et al 2009;Schmid 2010). The temporal coefficients, a i of the spectral discretized dynamical system are chosen such that the error is orthogonal to a subspace of H. Let { v i ∈ H| i = 1, .…”

Reduced-order representation of near-wall structures in the late transitional boundary layer

“…information on how much each identified structure is represented in the original data sequence. More details can be found in Rowley et al (2009), Schmid (2010 and Schmid, Violato & Scarano (2012). 10 -2 a n 10 -4 0 FIGURE 3.…”

“…In this respect, dynamic mode decomposition (DMD) (Schmid 2010) constitutes a suitable alternative to POD as it extracts spatial modes based on their single-frequency content rather than sorting them according to their contribution to the total energy. Dynamic mode decomposition has been applied in the context of turbulent channel flow to extract coherent structures from the flow by Mizuno et al (2011); however, the broadband nature of the spectra in that scenario makes it ill-suited for DMD.…”

Movement correction in DCE-MRI through windowed and reconstruction dynamic mode decomposition

“…DMD was originally introduced in the area of computational fluid dynamics (CFD) [28], specifically for analysing the sequential image data generated by nonlinear complex fluid flows [25][26][27]34]. The DMD decomposes a given image sequence into several images, called dynamic modes.…”

“…In contrast, the proposed W-DMD method runs standard DMD over a window of consecutive images; thus producing low-rank and sparse modes at each window of the image sequence, respectively, giving rise to W-DMD component-1 and component-2. The original DMD method introduced in [28] extracts modes from a sequence of images and interprets modes in the image space, whereas our reconstruction variant of the method (R-DMD) re-projects the DMD modes back into original image sequence, thereby stabilising the complex movements. Therefore, our contributions in this study are in (i) introducing the WR-DMD framework for the first time to reconstruct movement corrected, aligned images sequence.…”