A Domain Decomposition/Nash Equilibrium Methodology for the Solution of Direct and Inverse Problems in Fluid Dynamics with Evolutionary Algorithms

Abstract

The main goal of this paper is to present the application of a decentralization optimization principle from Game Theory to the solution of direct and inverse problems in Fluid Dynamics. It is shown in particular that multicriteria optimization methods "à la Nash" combine ideally with domain decomposition methods, with or without overlapping in order to solve complex problems. The resulting methodology is flexible and in the case of design problems has shown to perform well when using adjoint based techniques or evolutionary algorithms for the optimization. The above methodology is applied to the simulation and shape design optimization for flows in nozzles and around aerodynamical shapes.The results of various numerical experiments show the efficiency of the method presented here.