A One-Step Discrete Adjoint-Based Approach for Combined Design Optimization and A Posteriori Error Estimation

In recent years, CFD based design for flow related industrial applications, such as aerodynamics and turbomachinery, has increased in popularity. This has led to an intensive research towards adjoint formulations, both discrete and continuous, as this allows to compute the gradient of the objective (needed in gradient based optimization) 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 combined with output error control. In the present paper, we propose to combine both applications of the adjoint into a one-step combined design optimization and a posteriori error estimation methodology.