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.

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