Journal
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
Volume 31, Issue 2, Pages 111-126Publisher
SPRINGER
DOI: 10.1007/s00162-016-0408-7
Keywords
Reduced-order modeling (ROM); Galerkin projection; Dynamic mode decomposition (DMD); Continuous mode interpolation; CFD
Categories
Funding
- Polish National Centre of Science [2011/01/B/ST8/07264]
- Deutsche Forschungsgemeinschaft (DFG) [CRC 880]
- Bernd Noack Cybernetics Foundation
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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.
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