Hybrid Adjoint-based Robust Optimization Approach for Fluid-Dynamics Problems

A hybrid robust optimization approach is proposed, based on a generalized Adjoint Method of Moments (AMoM) coupled with a Multi-Objective Genetic Algorithm (MOGA). The gradient and Hessian of the objectives with respect to the uncertain parameters are used to evaluate expectancy and standard deviation of the quantities of interest. The required first and second order derivatives are computed through an automated numerical procedure including a non-linear, an adjoint and a linear solver. Initially, the performances of AMoM are assessed against some popular UQ techniques for quasi-1D inviscid ow through a supersonic diverging nozzle under dierent kinds of uncertainty (geometry, operating conditions, flow properties). Then the automated procedure for uncertainty quantification is coupled to a MOGA and applied to the robust inverse design of a quasi 1-D supersonic diverging nozzle. The proposed method is compared to other possible robust optimization strategies in terms of computational cost and solution accuracy.