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.
Keywords
Acknowledgements
This activity presented in this paper has been carried out within the project ACADEMIA (Advanced Computational Aerodynamic Environment for Multidisciplinary Integrated Analysis) partially funded by the Italian Ministry for University and Scientific Research.
Dedication: Two of the authors, D. Quagliarella and P.L. Vitagliano, wish to dedicate this paper to the memory of Professor Luciano Catalano who passed away before he could see the results of this research published. Luciano was the creator of the MAFD method presented, and helped to solve many of the problems related to the specific implementation of this work. His co-authors, however, wish to remember him for his qualities of humanity, kindness and unconditional availability, and are very honored and moved to have been able to enjoy his friendship.
Citation
Catalano, L.A., Quagliarella, D. and Vitagliano, P.L. (2015), "Aerodynamic shape design using hybrid evolutionary computing and multigrid-aided finite-difference evaluation of flow sensitivities", Engineering Computations, Vol. 32 No. 2, pp. 178-210. https://doi.org/10.1108/EC-02-2013-0058
Publisher
:Emerald Group Publishing Limited
Copyright © 2015, Emerald Group Publishing Limited