Efficient Deterministic Approaches for Aerodynamic Shape Optimization

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 using the adjoint flow equations. Here, one is independent of the number of design variables with respect to the numerical costs for determining the sensitivities. Another advantage of the adjoint approach is that one obtains accurate sensitivities and gets rid of the laborious tuning of the denominator step sizes for the finite differences.

Differentiation between continuous and discrete adjoint approaches is noted. 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. 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 multidisciplinary design optimization (MDO) problems will be discussed for aerostructure cases. Finally, we will discuss the so-called one-shot methods. Here, one breaks open the simulation loop for optimization.