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Improved extrapolation of steady turbulent aerodynamics using a non-linear POD-based reduced order model

Published online by Cambridge University Press:  27 January 2016

R. Zimmermann  and
S. Görtz
R. Zimmermann*
Affiliation:
Institute Computational Mathematics, TU Braunschweig, Germany
S. Görtz
Affiliation:
Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Germany
*
[email protected]
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Abstract

A reduced-order modelling (ROM) approach for predicting steady, turbulent aerodynamic flows based on computational fluid dynamics (CFD) and proper orthogonal decomposition (POD) is presented. Model-order reduction is achieved by parameter space sampling, solution space representation via POD and restriction of a CFD solver to the POD subspace. Solving the governing equations of fluid dynamics is replaced by solving a non-linear least-squares optimisation problem. The method will be referred to as LSQ-ROM method. Two approaches of extracting POD basis information from CFD snapshot data are discussed: POD of the full state vector (global POD) and POD of each of the partial states separately (variable-by-variable POD). The method at hand is demonstrated for a 2D aerofoil (NACA 64A010) as well as for a complete industrial aircraft configuration (NASA Common Research Model) in the transonic flow regime by computing ROMs of the compressible Reynolds-averaged Navier-Stokes equations, pursuing both the global and the variable-by-variable POD approach. The LSQ-ROM approach is tried for extrapolatory flow conditions. Results are juxtaposed with those obtained by POD-based extrapolation using Kriging and the radial basis functions spline method. As a reference, the full-order CFD solutions are considered. For the industrial aircraft configuration, the cost of computing the reduced-order solution is shown to be two orders of magnitude lower than that of computing the reference CFD solution.

Type
Research Article
Information
The Aeronautical Journal , Volume 116 , Issue 1184 , October 2012 , pp. 1079 - 1100
Copyright
Copyright © Royal Aeronautical Society 2012 

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