Joao Duarte Carrilho Miranda, VUB

Ajoint formulations have been extensively used for shape optimization problems as they allow to compute the gradient of the objective at the cost of roughly an extra single CFD simulation, and this independently of the number of design variables. As industrial design problems usually have many design variables, the adjoint approach outperforms the more  traditional approaches to find the sensitivities such as a finite differencing approach. Another application of the adjoint method is in adjoint-based a posteriori error estimation where the adjoint solution is used to estimate the error on the objective and to carry out grid adaptation. We propose to combine both applications of the adjoint into a one-step combined design optimization and a posteriori  error estimation methodology using a single adjoint solution. The developed approach is applied to relevant engineering problems, such as geometrical optimization of pipe flows.

The design variables are the shape coordinates and no parameterization is used. The results indicate a significant reduction of the computational costs compared to the standard optimization techniques.