Aerodynamic optimization utilizing control theory

This paper presents the method of aerodynamic optimization utilizing control theory, which is also called the adjoint method. The discrete adjoint equations are obtained from an unstructured cell-vortex finite-volume Navier-Stokes solver. The developed adjoint equations solver is verified by comparison of objective sensitivities with finite differences. An aerodynamic optimization system is developed combining the flow solver, adjoint solver, mesh deformation and a gradient-based optimizer. The surface geometry is parameterized using Free Form Deformation (FFD) method and a linear elasticity method is employed for the volume mesh deformation during optimization process. This optimization system is successfully applied to a design case of ONERA M6 transonic wing design.