Design method of aircraft boundary characteristics based on upwind adjoint equation

The boundary characteristics of an aircraft determine its safety and flight performance, and have always been the difficulty and focus of aircraft design. This paper aims to improve the accuracy, efficiency and robustness of the adjoint equation solution for complex flow problems by introducing the adjoint equation of the upwind format and different flux limiter processing forms, thereby expanding the application scope of the adjoint optimization method in the design of the boundary characteristics of aircraft. Firstly, the basic principle of discrete adjoint gradient solution is introduced. On this basis, the inviscid term of the adjoint equation and the variational form of its boundary conditions are derived. According to the processing method of the flux limiter, the adjoint equation with first-order accuracy, second-order accuracy and mixed accuracy is formed. Then, the boundary processing measures of the adjoint equation are studied. Through the ONERA M6 wing gradient accuracy and robustness verification example, the solution performance of the adjoint equation of the upwind format and the center format is compared, and the influence of the limiter and boundary processing measures on the convergence and gradient accuracy of the adjoint equation is analyzed. Through the cruise aerodynamic optimization design and boundary characteristics optimization design examples of the CRM wing-body assembly, the effectiveness of the solver for the cruise performance design and boundary characteristics design of the aircraft is verified. The calculation and design results show that the solution method of the upwind adjoint equation established in this paper is robust, has high gradient accuracy, and can be applied to solving the difficult problems of aircraft boundary characteristic design.