Adjoint-based sensitivity analysis by panel methods and CAS

Abstract

The work presented in this paper deals with the accuracy of the sensitivity derivatives of aerodynamic cost functions obtained by using an adjoint method. The accuracy of these gradients is evaluated by comparison with gradients computed via finite-differences in a straight-forward manner. The advantages of the use of an adjoint method become extremely clear since the computational effort incurred in the calculation of a complete gradient with respect to an arbitrary number of variables is independent of the number of variables and the only cost involved is the calculation of one flow solution and one adjoint solution, where the adjoint equation is a linear equation and, hence, of reduced complexity. In order to focus on the design and optimization procedure, we limit our study to one of the simplest flows: a subsonic potential flow over an airfoil section. First, for a generic objective function, we present a tool to automatically compute the gradient expression through adjoint techniques based on MAPLE, one of the most powerful computer algebra system (CAS). Second, exploiting the linearity of the governing equation, an adjoint solver is implemented based on the classical Douglas-Neumann panel method. The use of the solver is illustrated for a sample design calculation.