Projection-Based Model Order Reduction for Steady Aerodynamics

Abstract

Nonlinear model order reduction techniques for systems often make use of Proper Orthogonal Decomposition (POD). In this work a method based on POD, called Missing Point Estimation (MPE), is investigated. It is capable of efficiently simulating steady-state flows with the angle of attack as a system parameter. The basic idea of MPE is to project the governing equations onto the POD subspace in such a way that the resulting reduced order model does not have to evaluate the nonlinear right hand side at each and every grid point, but only at a few selected points. While the projection onto the POD subspace yields a reduced order model, the limitation to only few points actually achieves independence from the full order of the governing equations. To demonstrate the effectiveness of this method, numerical results for the simulation of inviscid, steady-state flows past a three-dimensional, complex airplane configuration are given.