Thel1-based sparsification of energy interactions in unsteady lid-driven cavity flow
| Autor: | Andrea Da Ronch, Davide Lasagna, Riccardo Rubini |
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| Rok vydání: | 2020 |
| Předmět: |
Scale (ratio)
Computer science Turbulence Mechanical Engineering Condensed Matter Physics 01 natural sciences Stability (probability) Projection (linear algebra) Discrete Fourier transform 010305 fluids & plasmas Flow (mathematics) Mechanics of Materials 0103 physical sciences A priori and a posteriori Statistical physics 010306 general physics Galerkin method |
| Zdroj: | Journal of Fluid Mechanics. 905 |
| ISSN: | 1469-7645 0022-1120 |
| Popis: | In this paper, sparsity-promoting regression techniques are employed to automatically identify from data relevant triadic interactions between modal structures in large Galerkin-based models of two-dimensional unsteady flows. The approach produces interpretable, sparsely connected models that reproduce the original dynamical behaviour at a much lower computational cost, as fewer triadic interactions need to be evaluated. The key feature of the approach is that dominant interactions are selected systematically from the solution of a convex optimisation problem, with a unique solution, and no a priori assumptions on the structure of scale interactions are required. We demonstrate this approach on models of two-dimensional lid-driven cavity flow at Reynolds number , where fluid motion is chaotic. To understand the role of the subspace utilised for the Galerkin projection in the sparsity characteristics, we consider two families of models obtained from two different modal decomposition techniques. The first uses energy-optimal proper orthogonal decomposition modes, while the second uses modes oscillating at a single frequency obtained from discrete Fourier transform of the flow snapshots. We show that, in both cases, and despite no a priori physical knowledge being incorporated into the approach, relevant interactions across the hierarchy of modes are identified in agreement with the expected picture of scale interactions in two-dimensional turbulence. Yet, substantial structural changes in the interaction pattern and a quantitatively different sparsity are observed. Finally, although not directly enforced in the procedure, the sparsified models have excellent long-term stability properties and correctly reproduce the spatio-temporal evolution of dominant flow structures in the cavity. |
| Databáze: | OpenAIRE |
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