Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models

Abstract

We present a model order reduction approach for parametrized laminar flow problems including viscous boundary layers. The viscous effects are captured by the incompressible Navier–Stokes equations in the vicinity of the boundary layer, whereas a potential flow model is used in the outer region. By this, we provide an accurate model that avoids imposing the Kutta condition for potential flows as well as an expensive numerical solution of a global viscous model. To account for the parametrized nature of the problem, we apply the reduced basis method. The accuracy of the reduced order model is ensured by rapidly computable a posteriori error estimates. The main contributions of this paper are the combination of an offline-online splitting with the domain decomposition approach, reducing both offline and online computational loads and a new kernel interpolation method for the approximation of the stability factor in the online evaluation of the error estimate. The viability of our approach is demonstrated by numerical experiments for the section of a NACA airfoil.