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 optimization problem in which flow variables and design variables are 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 feasiblility and optimality at the same time (all–at–once). This decoupling of variables typically makes the problem less nonlinear 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 are described. Implementation issues are presented and numerical results are given which indicate that the cost of solving the design problem is approximately six times the cost of solving a single analysis problem. Key words Airfoil design, optimization, computational fluid dynamics, Euler equations, nonlinear programming, optimal design