Aerodynamic design method based on N-S equations and discrete adjoint approach

One of the most important things in design optimization that based on gradient is to acquire the gradient quickly and accurately. A discrete adjoint approach is developed in this paper to get the gradient, and the flow governing equations are NS equations. Both the adjoint equations and the flow governing equations are solved by LU-SGS method. Examples show that this method acquire gradient quickly and accurately in both subsonic and transonic case. An airfoil is optimized using this method. Shockwave of the airfoil is weakened and the total drag is reduced. The test results show that the present method is reliable and efficient and is especially applicable in engineering.