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. 1. Introduction In spite of continuous improvement in computer resources, predicting the aerodynamic characteristics of aircraft using high fidelity computational fluid dynamics (CFD) remains a CPU intensive task. With the confirmed success of CFD in aerodynamic analysis, CFD technology has become a candidate for partially replacing wind tunnel testing in order to obtain aircraft stability and control characteristics. This calls for substantially more CPU capacity, however. For example, as discussed by Salas [1], a CFD database for use in 6-DOF flight simulation requires thousands of data points in the flight envelope. The same type of increase in CPU demand is observed in the aerodynamic and multidisciplinary design optimization communities, where thousands of CFD solutions are often required in typical design optimization studies. A viable alternative to meet this demand is surrogate models. Among the various methods available for constructing surrogate models from a reduced set of high fidelity solutions are reduced-order models which are based on POD. These models constitute a powerful tool for obtaining an approximate CFD solution over the entire domain. Such tools could be used in preliminary design phases because of their easiness of implementation and their low need in computational time. Engineers could easily use these tools to determine a few promising
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