Aerodynamic shape design using hybrid evolutionary computing and multigrid-aided finite-difference evaluation of flow sensitivities

Abstract

Purpose – The purpose of this paper is to propose an accurate and efficient technique for computing flow sensitivities by finite differences of perturbed flow fields. It relies on computing the perturbed flows on coarser grid levels only: to achieve the same fine-grid accuracy, the approximate value of the relative local truncation error between coarser and finest grids unperturbed flow fields, provided by a standard multigrid method, is added to the coarse grid equations. The gradient computation is introduced in a hybrid genetic algorithm (HGA) that takes advantage of the presented method to accelerate the gradient-based search. An application to a classical transonic airfoil design is reported. Design/methodology/approach – Genetic optimization algorithm hybridized with classical gradient-based search techniques; usage of fast and accurate gradient computation technique. Findings – The new variant of the prolongation operator with weighting terms based on the volume of grid cells improves the accuracy of the MAFD method for turbulent viscous flows. The hybrid GA is capable to efficiently handle and compensate for the error that, although very limited, is present in the multigrid-aided finite-difference (MAFD) gradient evaluation method. Research limitations/implications – The proposed new variants of HGA, while outperforming the simple genetic algorithm, still require tuning and validation to further improve performance. Practical implications – Significant speedup of CFD-based optimization loops. Originality/value – Introduction of new multigrid prolongation operator that improves the accuracy of MAFD method for turbulent viscous flows. First application of MAFD evaluation of flow sensitivities within a hybrid optimization framework.