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Minimum residual based model order reduction approach for unsteady nonlinear aerodynamic problems

Ripepi, M. and Zimmermann, R. and Görtz, Stefan (2016) Minimum residual based model order reduction approach for unsteady nonlinear aerodynamic problems. Data-Driven Model Order Reduction and Machine Learning (MORML 2016), 30 Mar - 1 Apr 2016, Stuttgart, Germany.

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Abstract

The advent and development of large-scale high-fidelity computational fluid dynamics (CFD) in aircraft design is requiring, more and more, procedures and techniques aimed at reducing its computational cost in order to afford accurate but fast simulations of, e.g., the aerodynamic loads. The adoption of reduced order modeling techniques in CFD represents a promising approach to achieve this goal. Several methods have been developed to obtain reduced order models (ROMs) for the prediction of steady aerodynamic flows using low-dimensional linear subspaces as well as nonlinear manifolds, whose performances may be further improved by applying hyper-reduction procedures. In this talk, a model order reduction approach for unsteady aerodynamic applications is presented. The problem of finding the CFD ROM is formulated as a non-linear least-squares optimization problem, by searching in a subspace for an approximate flow solution having a minimum norm least-squares solution for the corresponding unsteady (flow solver) residual. The reduced basis for representing the reduced-order solutions of the governing equations is obtained through a Proper Orthogonal Decomposition (POD) applied to a given set of solutions of the full-order model at different time steps. The arising nonlinear least-squares problem for the POD coefficients is solved by using a Levenberg-Marquardt (LM) algorithm. A Broyden update procedure is employed to approximate the Jacobian of the reduced-order system of equations, and it is further exploited to reduce the computational costs to generate the approximate Hessian matrix for the LM procedure. In addition, the potential of masked projection approaches, such as the missing point estimation (MPE), is going to be investigated. The proposed approach is demonstrated for the Navier-Stokes equations by modeling the transonic flow around the LANN wing oscillating in pitch at different reduced frequencies.

Item URL in elib:https://elib.dlr.de/105983/
Document Type:Conference or Workshop Item (Speech)
Title:Minimum residual based model order reduction approach for unsteady nonlinear aerodynamic problems
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Ripepi, M.matteo.ripepi (at) dlr.deUNSPECIFIED
Zimmermann, R.Ralf.Zimmermann (at) tu-braunschweig.deUNSPECIFIED
Görtz, StefanStefan.Goertz (at) dlr.deUNSPECIFIED
Date:30 March 2016
Refereed publication:No
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:model reduction, proper orthogonal decomposition, missing point estimation, greedy procedure, unsteady aerodynamic
Event Title:Data-Driven Model Order Reduction and Machine Learning (MORML 2016)
Event Location:Stuttgart, Germany
Event Type:Workshop
Event Dates:30 Mar - 1 Apr 2016
Organizer:University of Stuttgart, Germany
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering
Deposited By: Ripepi, Matteo
Deposited On:07 Sep 2016 08:55
Last Modified:07 Sep 2016 08:55

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