Optimum Shape Design for Unsteady Flows with Time-Accurate Continuous and Discrete Adjoint Methods

This paper presents an adjoint method for the optimal control of unsteady flows. The goal is to develop the continuous and discrete unsteady adjoint equations and their corresponding boundary conditions for the timeaccuratemethod. First, this paper presents the complete formulation of the time-dependent optimal design problem. Second, we present the time-accurate unsteady continuous and discrete adjoint equations. Third, we present results that demonstrate the application of the theory to a two-dimensional oscillating airfoil. The results are comparedwith a multipoint approach to illustrate the added benefit of performing full unsteady optimization.