A Second-order sensitivity equation method for laminar flow

Abstract

This paper presents a general Continuous Sensitivity Equation (CSE) method for computing first and second-order flow sensitivities for the incompressible Navier–Stokes equations. The sensitivity equations and boundary conditions are developed for value parameters that do not affect the geometry of the computational domain. Applications are thus restricted to the simpler case of value parameters. The flow and sensitivity equations are solved by an adaptive finite element method. The proposed methodology is verified on a problem with a closed form solution. The verified code is then applied to compute first- and second-order flow sensitivities of an airfoil with respect to the angle of attack and the free-stream velocity. We demonstrate the use of sensitivities for fast first- and second-order evaluations of nearby flows. The methodology is also used to perform second-order uncertainty analysis.