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Theoretical and Computational Fluid Dynamics

, Volume 31, Issue 2, pp 111–126 | Cite as

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

  • Witold Stankiewicz
  • Marek Morzyński
  • Krzysztof Kotecki
  • Bernd R. Noack
Open Access
Original Article

Abstract

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier–Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier–Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

Keywords

Reduced-order modeling (ROM) Galerkin projection Dynamic mode decomposition (DMD) Continuous mode interpolation CFD 

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Chair of Virtual EngineeringPoznan University of TechnologyPoznańPoland
  2. 2.UPR 3251LIMSI-CNRSOrsay CedexFrance
  3. 3.Institut fr StrömungsmechanikTechnische Universität BraunschweigBraunschweigGermany

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