Distributed Optimization using Virtual and Real Game Strategies for Aerodynamic Design
Résumé
This report approaches the question of multi-disciplinary optimization for optimum shape design in Aerodynamics using game theory. The employed optimizer is based on control theory, which produces very robust optimization algorithms particularly well suited for problems of constrained optimizations. We perform an airfoil drag reduction under the constraint of constant , and a lift maximization under the constraint of constant C_d . Here, we introduce a scalar adjoint variable to satisfy these constraint- s. Comparing with the unconstrained case, these constraints can be easily implemented by introducing an additional scalar algebraic adjoint equation. Furthermore, the above methodological ingredients are combined with a formulation derived from Game Theory to treat multi-point airfoil optimization- . Airfoil shapes are optimized according to various aerodynamic criteria (under conflict). Each `player' in a symmetric Nash game optimizes one's own criterion using information provided by the others. The Nash equilibrium then corresponds to the solution of a multi-point optimization. Subsonic/Trans- onic flows around lifting airfoils are analyzed by Eulerian computations. Several kinds of airfoil splittings and aerodynamic design cases are considered illustrating virtual and real game strategies. Successful design results confirm the validity and efficency of the present design method in a parallel computing environment.
Loading...