Nonlinear Elimination in Aerodynamic Analysis and Design Optimization

Recent emphasis on reduction of design cycle time and cost in the design of commercial aircraft has sparked a renewed interest in design optimization in aerodynamic s, structures, and aeroelastics. The constrained aerodynamic optimization problem is closely related to the problem of solving nonlinear systems of equations. In applying Newton’s method to steady-state compressible CFD analysis problems, the nonlinear elimination method has been remarkably successful. In this paper we consider the implications of this experience for design optimization formulations in the general case of state equation equality constraints. This relationship between nonlinear equation solving and design optimization is illustrated by drawing on computational examples from the TRANAIR compressible CFD code. We first discuss various formulations of the PDE constrained optimization problem related to the Lagrange Newton method and the multiplier free version implementation in TRANAIR. We then discuss the nonlinear elimination method and its application to a simple nozzle problem. This method is then applied to derive various globalization methods in design optimization which are illustrated by a computational example in airfoil design. Finally, we discuss some remaining limitations and issues.

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