Work reported herein was sponsored by NASA under contract NAS 2-96027 between NASA and the Universities Space Research Association (USRA). ABSTRACT An aerodynamicshape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory In order to facilitate the integration of these high fidelity CFD approaches into futuremulti-disciplinary optimization (MIX)) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies [8, 9, 10, 11, 19, 15, 20, 21, 22, 23, 1], we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations.

describes a shape optimization method for aerodynamic design problems involving complex aircraft configurations and multiple design points that are subject to geometric constraints. The aerodynamic performance is evaluated using a set of high-fidelity governing equations discretized on body-conforming multiblock meshes. The design process is greatly accelerated through the use of an adjoint method for the calculation of sensitivity information and by means of a parallel implementation for distributed memory computers. This paper focuses on the details of the development and implementation of the complete design algorithm. A general adjoint formulation of the design optimization problem is presented along with a detailed derivation of the adjoint system for the Euler equations. The multiblock approach for the flow and adjoint solution algorithm and the mesh perturbation procedure are described. The extension of this approach to treat multipoint and constrained shape optimization of complete aircraft configurations is also discussed. Finally, the details of the parallel implementation are examined. Nomenclature Aj= Cartesian flow Jacobian matrix in the ith direction C A , C N = coefficients of axial and normal force C D , C L = coefficients of drag and lift C f = contravariant flow Jacobian matrix in the /th directionenergy F = boundary shape Fi = contravariant inviscid fluxes / = Cartesian inviscid fluxes G = gradient vector H = total enthalpy I = cost function J = det(AT) K tj = mesh transformation Jacobian matrix components Moo = freestream Mach number p = static pressure /?oo = freestream static pressure Q.j = velocity transformation matrix R = governing equations, residual S = surface area S x , S y , S. = projected surface areas in Cartesian coordinate directions t = time U f = contravariant velocity components Ui = Cartesian velocity components W -conservative contravariant flow variables \v -conservative Cartesian flow variables Xi = Cartesian coordinates a = angle of attack y = ratio of specific heats, C P /C V = first variation -Kronecker delta function = cost function weights for the /th flow condition £ = computational coordinates p = fluid density \\f = Lagrange multiplier, costate, or adjoint variable

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