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

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

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