Reduced-Order Model for Viscous Aerodynamic Flow Past an Airfoil

A method is presented to obtain reduced-order models of multiparametric, steady, transonic aerodynamic flows around two-dimensional airfoils. The method is based on proper orthogonal decomposition and appropriate projection on the proper orthogonal decomposition manifold of the governing equations and boundary conditions, and it includes various ingredients that are new in this field. Proper orthogonal decomposition modes are obtained from a set of snapshots calculated by computational fluid dynamics based on the compressible Navier―Stokes equations and a turbulence model, but projection on the proper orthogonal decomposition manifold is made using the inviscid Euler equations, which makes the method independent of the computational fluid dynamics scheme; projection is made using only a limited number of mesh points, obtaining quite good results. Shock waves are treated specifically in the proper orthogonal decomposition description, to avoid the need of using a too-large number of snapshots. The method is checked and discussed on a specific aerodynamic problem.