Airfoil Design by an All-at-once Method*

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Abstract
The all-at-once approach is implemented to solve an optimum airfoil design problem. The airfoil design problem is formulated as a constrained optimization problem in which flow variables and design variables arc viewed as independent and the coupling steady state Euler equation is included as a constraint, along with geometry and other constraints. In this formulation, the optimizer computes a sequence of points which tend toward feasibility and optimalily at the same lime (all-at-once). This decoupling of variables typically makes the problem less non-linear and can lead to more efficient solutions. In this paper an existing optimization algorithm is combined with an existing flow code. The problem formulation, its discretization, and the underlying solvers arc described. Implementation issues arc presented and numerical results are given which indicate that the cost of solving the design problem is appropriately six times the cost of solving a single analysis problem.

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