In this paper, gradient/Hessian-enhanced surrogate models have been developed based on Kriging approaches. The gradient/Hessian-enhanced Kriging methods have been developed based on direct and indirect formulations. The efficiencies of these methods are compared by analytical function fitting, aerodynamic data modeling and 2D airfoil drag minimization problems. For the aerodynamic problems, efficient CFD gradient/Hessian calculation methods are utilized that make use of adjoint and automatic differentiation techniques. The gradient/Hessian-enhanced surrogate models are shown to be useful in the development of efficient design optimization, aerodynamic database construction, and uncertainty analysis.

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This paper presents a general framework to derive a discrete adjoint method for the optimal control of unsteady flows. The complete formulation of a generic time-dependent optimal design problem is introduced and it is outlined how to derive the discrete set of adjoint equations in a general approach. Results are shown that demonstrate the application of the theory to the drag minimization of viscous flow around a rotating cylinder, and to the remote inverse design of laminar flow around the multi-element NLR 7301 configuration at a high angle of attack. In order to reduce the considerable computational costs of unsteady optimization, the use of bigger time steps over transitional or unphysical adjusting periods as well as omitting time steps while recording the flow solution are investigated and are shown to work well in practice.

This paper presents a general framework to derive a discrete adjoint method for the optimal control of unsteady flows. First, we present the complete formulation of the timedependent optimal design problem and outline how to derive the discrete set of adjoint equations in a general approach. After that we present results that demonstrate the application of the theory to one-and two-dimensional inverse pulseshape designs, the data assimilation problem in a shock-tube, the drag minimization of viscous flow around a rotating cylinder, and the remote inverse design of a turbulent flow around a NACA0012 airfoil at a high angle of attack.