Airfoil design by an all-at-once method

The all-at-once approach is implemented to solve an optimum airfoil design problem. The airfoil design problem is formulated as a constrained optimiza tion problem in which flow variables and design variables are viewed as ind ependent and the coupling steady stale Euler equation is included as a cons traint, along with geometry and other constraints. In this formulation, the optimizer computes a sequence of points which tend toward feasibility and optimality at the same time (all-at-once). This decoupling of Variables typ ically makes the problem less non-linear and can lead to more efficient sol utions. In this paper an existing optimization algorithm is combined with a n existing flow code. The problem formulation, its discretization, and the underlying solvers are described. Implementation issues are presented and n umerical results are given which indicate that the cost of solving the desi gn problem is approximately six times the cost of solving a single analysis problem.