We present a new approach to simulating unsteady fluid flows, with only very few degrees of freedom, by employing directly eigenmodes extracted from digital particle image velocimetry experimental data. In particular, we formulate standard Galerkin and nonlinear Galerkin approximations of the incompressible Navier-Stokes equations using hierarchical empirical eigenfunctions extracted from an ensemble of flow snapshots. We demonstrate that standard Galerkin approaches produce simulations capable of capturing the short-term dynamics of the flow, but nonlinear Galerkin projections are more effective in capturing both the short- and long-term dynamics, leading to bounded solutions. These ­ findings are documented by applying these approaches to flow past a stationary circular cylinder at Reynolds number 610.

References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Feng, Li-Hao; Wang, Jin-Jun: Modification of a circular cylinder wake with synthetic jet: vortex shedding modes and mechanism (2014)
  2. Venturi, Daniele: A fully symmetric nonlinear biorthogonal decomposition theory for random fields (2011)
  3. Suzuki, Takao; Ji, Hui; Yamamoto, Fujio: Instability waves in a low-Reynolds-number planar jet investigated with hybrid simulation combining particle tracking velocimetry and direct numerical simulation (2010)
  4. Aquino, W.; Brigham, J.C.; Earls, C.J.; Sukumar, N.: Generalized finite element method using proper orthogonal decomposition (2009)
  5. Drazen, David A.; Melville, W.Kendall: Turbulence and mixing in unsteady breaking surface waves (2009)
  6. Minor, G.; Djilali, N.; Sinton, D.; Oshkai, P.: Flow within a water droplet subjected to an air stream in a hydrophobic microchannel (2009)
  7. Buffoni, M.; Camarri, S.; Iollo, A.; Lombardi, E.; Salvetti, M.V.: A non-linear observer for unsteady three-dimensional flows (2008)
  8. Venturi, Daniele; Wan, Xiaoliang; Karniadakis, George Em: Stochastic low-dimensional modelling of a random laminar wake past a circular cylinder (2008)
  9. Voorhees, A.; Dong, P.; Atsavapranee, P.; Benaroya, H.; Wei, T.: Beating of a circular cylinder mounted as an inverted pendulum (2008)
  10. Aquino, Wilkins: An object-oriented framework for reduced-order models using proper orthogonal decomposition (POD) (2007)
  11. Hsu, T.Y.; Eloranta, H.; Saarenrinne, P.; Wei, T.: Turbulent flow through a rectangular duct with a partially blocked exit (2007)
  12. Konstantinidis, Efstathios; Balabani, Stavroula; Yianneskis, Michael: Bimodal vortex shedding in a perturbed cylinder wake (2007)
  13. Liebe, Roland J. (ed.): Flow phenomena in nature. Vol. 2: Inspiration, learning and application. Dedicated to Prof. Wolfgang Liebe (2007)
  14. Liu, Dong; Wu, Chin; Linden, Karl; Ducoste, Joel: Numerical simulation of UV disinfection reactors: evaluation of alternative turbulence models (2007)
  15. Sengupta, T. K.; Lim, T. T.; Sajjan, Sharanappa V.; Ganesh, S.; Soria, J.: Accelerated flow past a symmetric aerofoil: experiments and computations (2007)
  16. Siddiqui, M.H.Kamran; Loewen, Mark R.: Characteristics of the wind drift layer and microscale breaking waves (2007)
  17. Wu, Longhua: An improved algorithm for DPIV correlation analysis (2007)
  18. Gunes, Hasan; Sirisup, Sirod; Karniadakis, George Em: Gappy data: to krig or not to krig? (2006)
  19. Hörschler, I.; Brücker, Ch.; Schröder, Wolfgang; Meinke, Matthias: Investigation of the impact of the geometry on the nose flow (2006)
  20. Krueger, Paul S.; Dabiri, John O.; Gharib, Morteza: The formation number of vortex rings formed in uniform background co-flow (2006)

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