Model-Based Adaptive MOR Framework for Unsteady Flows Around Lifting Bodies

Abstract

The problem of performing accurate reconstructions of vortex-dominated unsteady flows by means of reduced basis methods is studied. When faced with the necessity of reconstructing the flow field over a specified time window, a method that aims at automatically and adaptively selecting the most accurate reduction technique among a collection of models is presented. The rationale behind the development of such an adaptive framework is to try to cope with the potential loss of important dynamic information that accompanies classical methods, e.g., proper orthogonal decomposition, where snapshots are treated as statistically independent observation of the dynamical system at study. The adaptive framework will be assessed with respect to two different ways of estimating the reconstruction error by the various methods. One method, referred to as direct error, will employ additional snapshots and will compare explicitly the reduced solution with the reference data. The second method will instead consider a finite volume discretization of the equations and evaluate the error in terms of the unsteady residual of the reduced solution. A backward differencing formula will be used to ensure second-order accuracy in the estimation of the residual. Emphasis will be put on the comparative assessment of the two error estimation methods with respect to the identification of the most suitable reduced method to be used for the reconstruction at a specific instant of time. Problems of relevance to aircraft aerodynamics will be considered such as the impulsive start of 2D airfoils in high-lift configurations.