Aerodynamic adjoint-based optimization design method for aircraft based on low-dissipation scheme

In aerodynamic discrete adjoint optimization design systems for aircraft, the accuracy and robustness of the flow field transport equations and adjoint equations are primarily influenced by the numerical discretization schemes used for the inviscid terms. Since the adjoint equations solve the differential information of the flow field, the adjoint variables are more sensitive than the flow field transport variables, making the proper treatment of inviscid terms critically important. To address this issue, the discrete adjoint equations and sensitivity equations based on the AUSMPW+ scheme were systematically derived, and a novel discrete adjoint optimization method employing the low-dissipation AUSMPW+ scheme was proposed. The effectiveness of the proposed method was thoroughly validated through representative numerical examples, including the transonic M6 wing and the NASA common research model (CRM) wing-body configuration. The optimization results achieved remarkable total drag reductions of 28.1 counts and 32.3 counts, respectively. Extensive computational and design results consistently demonstrate that the adjoint equation solver using the low-dissipation scheme exhibits excellent robustness and high accuracy in gradient calculations. This method is applicable to three-dimensional, complex, high-precision flow field solutions and aerodynamic optimization design for modern aircraft configurations, providing a reliable and efficient numerical tool for large-scale design variable optimization problems in practical engineering applications.