TY - JOUR
T1 - On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body
AU - Östh, Jan
AU - Noack, Bernd R.
AU - Krajnović, Siniša
AU - Barros, Diogo
AU - Borée, Jacques
N1 - Publisher Copyright:
© 2014 Cambridge University Press.
PY - 2014/4/10
Y1 - 2014/4/10
N2 - 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.
AB - 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.
KW - low-dimensional models
KW - turbulence simulation
KW - wakes
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U2 - 10.1017/jfm.2014.168
DO - 10.1017/jfm.2014.168
M3 - Article
AN - SCOPUS:84906881702
VL - 747
SP - 518
EP - 544
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
IS - 3
ER -