Aiaa 2003-3875 Optimum Shape Design for Unsteady Flows Using Time Accurate and Non-linear Frequency Domain Methods

This paper presents an adjoint method for the optimum shape design of unsteady flows. The goal is to develop a set of discrete unsteady adjoint equations and their corresponding boundary conditions for both the time accurate and non-linear frequency domain methods. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the time accurate and non-linear frequency domain adjoint equations. Third, we present results that demonstrate the application of the theory to a two-dimensional oscillating airfoil. Fourth, we compare the gradients between the two methods.