Global approximation and optimization using adjoint computational fluid dynamics codes

Approximation methods have found increasing use in the optimization of complex engineering systems. The approximation method provides a surrogate model that, once constructed, can be used in lieu of the original expensive model for the purposes of optimization. These approximations may be defined locally, for example, a low-order polynomial response surface approximation that employs trust region methodology during optimization, or globally, by the use of techniques such as kriging. Adjoint methods for computational fluid dynamics have made it possible to obtain sensitivity information on the model's response without recourse to finite differencing. This approach then allows for an efficient local optimization strategy where these sensitivities are utilized in gradient-based optimization. The combined use of an adjoint computational fluid dynamics code with approximation methods (incorporating gradients) for global optimization is shown. Several approximation methods are considered. It is shown that an adjoint-based approximation model can provide increased accuracy over traditional nongradient-based approximations at comparable cost, at least for modest numbers of design variables. As a result, these models are-found to be more reliable for surrogate assisted optimization.