This work discusses an approach, rst-order approximationand model management optimization (AMMO), for solving design optimization problems that involve computationally expensive simulations. AMMO maximizes the use of lower-delity, cheaper models in iterative procedures with occasional, but systematic, recourse to higherdelity, more expensive models for monitoring the progress of design optimization. A distinctive feature of the approach is that it is globally convergent to a solution of the original, high-delity problem. Variants of AMMO based on three nonlinear programming algorithms are demonstrated on a three-dimensional aerodynamic wing optimization problem and a two-dimensionalairfoil optimizationproblem. Euler analysison meshes of varying degrees of re nement provides a suite of variable-delity models. Preliminary results indicate threefold savings in terms of high-delity analyses for the three-dimensional problem and twofold savings for the two-dimensional problem. Nomenclature C D = drag coef cient C L = lift coef cient C l = rolling moment coef cient C M = pitching moment coef cient c E = equality constraints c I = inequality constraints f = objective function M 1 = freestream Mach number S = semispan wing planform area x; x L ; x U = design variables and bounds ® = angle of attack 1 = trust-region radius

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This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD code. Given uncertainties in statistically independent, random, normally distributed input variables, a first-and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first-and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving firstorder sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

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This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics.