Non-linear reduced order models for steady aerodynamics

A reduced order modelling approach for predicting steady aerodynamic flows and loads data based on Computational Fluid Dynamics (CFD) and global Proper Orthogonal Decomposition (POD), that is, POD for multiple different variables of interest simultaneously, is presented. A suitable data transformation for obtaining problemadapted global basis modes is introduced. Model order reduction is achieved by parameter space sampling, reduced solution space representation via global POD and restriction of a CFD flow solver to the reduced POD subspace. Solving the governing equations of fluid dynamics is replaced by solving a non-linear least-squares optimization problem. Methods for obtaining feasible starting solutions for the optimization procedure are discussed. The method is demonstrated by computing reduced-order solutions to the compressible Euler equations for the NACA 0012 airfoil based on two different snapshot sets; one in the subsonic and one in the transonic flow regime, where shocks occur. Results are compared with those obtained by POD-based interpolation using Kriging and the Thin Plate Spline method (TPS).