Model order reduction for steady aerodynamics of high-lift configurations

Abstract

In aerodynamic applications, many model reduction methods use proper orthogonal decomposition (POD). In this work, a POD-based method, called missing point estimation (MPE), is modified and applied to steady-state flows with variation of the angle of attack. The main idea of MPE is to select a subset of the computational grid points (control volumes) and to limit the governing equations to this subset. Subsequently, the limited equations are projected onto the POD subspace. This approach has the advantage that the nonlinear right-hand side of the governing equations has to be evaluated only for a small number of points (control volumes) in contrast to POD, for which the full right-hand side has to be evaluated. An error estimation for MPE in the continuous ODE setting is tackled. Numerical results are presented for the Navier–Stokes equations for two different industrially relevant, two-element high-lift airfoils, one which is normally adopted during landing and the other during take-off.