The boundary condition of aerodynamic optimization based on control theory

In aerodynamic optimization design, gradient optimization method is a popular optimization algorithm, but with the increase of design variables, the amount of calculation of gradient also increases. The advantage of gradients solution based on control theory is that gradients of all design variables can be obtained at one time. Optimization based on control theory is also called adjoint optimization design. The gradient is obtained by solving the first flow equation and the first adjoint equation. Objective function is related to boundary condition, and different objective function corresponds to different boundary condition. The processing of boundary condition is a key technology of adjoint optimization design. In this paper, three kinds of wall boundary conditions are derived, which are the reverse design of pressure distribution, the optimal design of drag reduction, and the constant lift coefficient. The adjoint flow field has no physical significance, but because the wall boundary condition is the source term of the adjoint equation, the adjoint flow field has certain mathematical meaning.