Optimum Shape Design for Unsteady Three- Dimensional Viscous Flows Using a Non- Linear Frequency Domain Method

This paper presents an adjoint method for the optimum shape design of unsteady three-dimensional viscous flows. The goal is to develop a set of discrete unsteady adjoint equations and the corresponding boundary condition for the non-linear frequency domain method. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the non-linear frequency domain adjoint equations for three-dimensional viscous transonic flows. Third, we present results that demonstrate the application of the theory to a three-dimensional wing.