Reduced-order modeling (ROM) of transient fluid flows using the proper orthogonal decomposition (POD) was studied. Particular attention was given to incompressible, unsteady flow over a two-dimensional NACA0015 airfoil in the laminar regime. When the airfoil sheds vortices, a transient blowing through a jet placed at the 10% chord location was imposed. POD modes were derived from the numerical solution of the flow obtained using an hp-finite element method. The ROM was obtained by a streamwise-upwind-Petrov-Galerkin (SUPG) projection of the incompressible Navier–Stokes equations onto the space spanned by the POD modes.

The extraction of accurate POD-based reduced order model of this flow was explored using three different POD mode generation methods. The first approach was the split method, which superposes modes derived from simulations of the blowing jet with no flow and simulations of the baseline flow with no jet. The second method combined POD modes derived from simulations having both the jet and flow with modes obtained from simulation of only the flow. These modes were generated after the simulations reached the periodic state. The third and newly proposed approach was to generate a set of modes called “Generalized POD basis functions.” These modes were derived from simulations where the jet’s flow amplitude is varied slowly. For each method, the results were compared with detailed Finite Element solutions and the accuracy and efficiency of different methods were evaluated. The newly proposed “Generalized POD basis functions” approach predicted the transient response of the system most accurately.

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