Investigation on the weighted product method using adjoint CFD

Abstract

Engineers in the field of aerodynamics today continuously strive to improve their designs to increase both their operational effectiveness and their market appeal. In the absence of an optimization approach, the decisions during a design process mainly rely on the judgment of experienced personnel, researchers, and engineers. However, the performance of a system can be improved by with the help of numerical optimization methods. Through several past studies, it is know that adjoint methods outperform other relevant optimization methods and hence, they often used in aerodynamic shape optimization. In this talk, the focus would mainly lie on the multi-objective optimization used adjoint Computational Fluid Mechanics(CFD). The multi-objective optimization is nowadays one of the main challenges faced by the mathematicians and engineers in the field of aerodynamics today. The adjoint Computational Fluid Mechanics (CFD) are based on the calculus of variations and the use of Lagrange multipliers. This gives us the scope to obtain an efficient tool for optimization with respect to multi-objective functions and prescribed constraints. Hence, an optimization procedure which is based on multi-objective approach can be applied to adjoint CFD to improve their the performance. The one of the state of art technique for multi-objective optimization is the weighted-sum method. From studies we perform in the past it is known that, applying this approach with adjoint method faces difficulties in searching the appropriate weighting factors and of one of the weighting factors dominates. Hence, here we consider a more effective alternative approach the so-called weighted product method and cmpare its peformance with the weighted-sum method with respect to above mentioned drawbacks. It is shown below that the presented weighted product method is capable of finding combinations that are located closer to the utopia point compared to those of the weighted-sum method.