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Model order reduction using sparse coding exemplified for the lid-driven cavity

  • Rohit Deshmukh (a1), Jack J. McNamara (a1), Zongxian Liang (a1), J. Zico Kolter (a2) and Abhijit Gogulapati (a1)...
Abstract

Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

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Email address for correspondence: mcnamara.190@osu.edu
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M. Ilak , S. Bagheri , L. Brandt , C. W. Rowley  & D. S. Henningson 2010 Model reduction of the nonlinear complex Ginzburg–Landau equation. SIAM J. Appl. Dyn. Syst. 9 (4), 12841302.

M. R. Jovanović , P. J. Schmid  & J. W. Nichols 2014 Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26 (2), 024103.

I. Kalashnikova , W. B. van Bloemen , S. Arunajatesan  & M. Barone 2014 Stabilization of projection-based reduced order models for linear time-invariant systems via optimization-based eigenvalue reassignment. Comput. Meth. Appl. Mech. Engng 272, 251270.

C. W. Rowley 2005 Model reduction for fluids, using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos 15 (03), 9971013.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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