Adjoint approaches in aerodynamic shape optimization and MDO context

Because detailed aerodynamic shape optimizations still suffer from high computational costs, efficient optimization strategies are required. Regarding the deterministic optimization methods, the adjoint approach is seen as a promising alternative to the classical finite difference approach. With the adjoint approach the sensitivities needed for the aerodynamic shape optimization can be efficiently obtained by solution of the adjoint flow equations. Here, one is independent of the number of design variables with respect to the numerical costs for determining the sensitivities. One distinguishes between continuous and discrete adjoint approaches. In the continuous case one formulates the optimality condition first, then derives the adjoint problem and finally does the discretization of the so obtained adjoint flow equations. On the other hand, in the discrete case one takes the discretized flow equations for the derivation of the discrete adjoint problem. This can be automated by so called algorithmic differentiation (AD) tools. The different adjoint approaches will be explained for single disciplinary aerodynamic shape optimization first and then their extension to MDO problems will be discussed for aero/structure cases