On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body

By J. Osth, Bernd R. Noack, Sinivsa Krajnovi'c, D. Barros, Jacques Bor'ee. Journal of Fluid Mechanics, 2013

213 citations recorded by the source corpus.

Abstract We investigate a hierarchy of eddy-viscosity terms in proper orthogonal decomposition (POD) Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to large eddy simulation (LES) data for a flow around a vehicle-like bluff body called an Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (J. Fluid Mech., vol. 260, 1994a, pp. 351–375; J. Fluid Mech. vol. 275, 1994b, pp. 257–283). Robustness of the model solution with respect to initial conditions, eddy-viscosity values and model order is achieved only for state-dependent eddy viscosities as proposed by Noack, Morzyński & Tadmor (Reduced-Order Modelling for Flow Control, CISM Courses and Lectures, vol. 528, 2011). Only the POD system with state-dependent modal eddy viscosities can address all challenges of the flow characteristics. All parameters are analytically derived from the Navier–Stokes-based balance equations with the available data. We arrive at simple general guidelines for robust and accurate POD models which can be expected to hold for a large class of turbulent flows.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9a66e91d64a3a89692ea892d91beb496bb3037bb

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Citations in the corpus

Experimental characterization of the unsteady natural wake of the full-scale square back Ahmed body: flow bi-stability and spectral analysis (2015, background): “(2014) and Östh et al. (2014). Once again, this (9) E (”
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, background): “Turbulence is an important high-dimensional system that exhibits multiscale phenomena [19], [88], [89].”
Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes (2016, methodology): “Subsequent studies have addressed the effect of small scales in a high-lift configuration (Luchtenburg et al. 2009) and turbulent fluctuations in a complex bluff-body wake (Östh et al. 2014; Protas et al. 2015).”
Machine Learning Control – Taming Nonlinear Dynamics and Turbulence (2016, background): “scales to arrive at the converged actuated state [21, 205].”
Compressive Sensing and Low-Rank Libraries for Classification of Bifurcation Regimes in Nonlinear Dynamical Systems (2013, methodology): “Alternative methods for stabilizing POD by adding additional modes and closure terms have been investigated [3, 33].”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, unknown): “113”
Bluff body drag manipulation using pulsed jets and Coanda effect (2015, methodology): “This has been verified by the data from the large eddy simulation analyzed in Östh et al. (2014).”
Cluster-based reduced-order modelling of a mixing layer (2013, methodology): “A further analysis of the forces reveals that the two semimodal states are associated with an increase in the magnitude of the side force which was also found by Grandemange et al. (2013) and Östh et al. (2013) for the same data.”