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International Journal of Aerospace Engineering
Volume 2013, Article ID 928904, 11 pages
http://dx.doi.org/10.1155/2013/928904
Research Article

Interpolation of Transonic Flows Using a Proper Orthogonal Decomposition Method

École Polytechnique de Montréal, Department of Mechanical Engineering, 2900 Boulevard Edouard-Montpetit, Montréal, QC, Canada H3T 1J4

Received 9 April 2013; Revised 23 July 2013; Accepted 25 July 2013

Academic Editor: R. Ganguli

Copyright © 2013 Benoit Malouin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A proper orthogonal decomposition (POD) method is used to interpolate the flow around an airfoil for various Mach numbers and angles of attack in the transonic regime. POD uses a few numerical simulations, called snapshots, to create eigenfunctions. These eigenfunctions are combined using weighting coefficients to create a new solution for different values of the input parameters. Since POD methods are linear, their interpolation capabilities are quite limited when dealing with flow presenting nonlinearities, such as shocks. In order to improve their performance for cases involving shocks, a new method is proposed using variable fidelity. The main idea is to use POD to interpolate the difference between the CFD solution obtained on two different grids, a coarse one and a fine one. Then, for any new input parameter value, a coarse grid solution is computed using CFD and the POD interpolated difference is added to predict the fine grid solution. This allows some nonlinearities associated with the flow to be introduced. Results for various Mach numbers and angles of attack are compared to full CFD results. The variable fidelity-based POD method shows good improvement over the classical approach.