基于三维非结构混合网格的离散伴随优化方法

伴随优化方法在优化过程中不受设计变量个数的限制，有巨大的工程应用前景。基于非结构混合网格技术，采用雷诺平均Navier-Stokes方程、离散伴随优化方法以及自由形面变形（FFD）技术，建立了飞行器气动外形优化设计系统。离散伴随方程采用公式推导的方法直接获取，并运用LU-SGS迭代求解。通过与差分结果进行比较的方式，对通量的雅可比矩阵和目标函数敏感导数开展了确认，并对文中黏性通量项、限制器以及湍流黏性系数的近似处理方法做了分析对比，验证了近似处理方法的合理性和可行性。采用建立的优化系统，完成了ONERA M6机翼在跨声速条件下的减阻优化，并比较了有无容积约束下优化结果的差别。模拟验证结果表明，建立的飞行器气动外形优化设计系统具有较高的可靠性和有效性，可以用于三维飞行器外形的减阻优化。

Discrete Adjoint Optimization Method for 3D Unstructured Grid

Because solving adjoint equation does not depend on the number of design variables, there is no relationship between the calculation amount of iterative optimization and the number of design variables. Based on the unstructured grid, a discrete adjoint solver is developed for a 3D Reynolds-averaged Navier-Stokes solver. Free-form deformation (FFD) technology is implemented to modify the mesh. Discrete adjoint equation can be acquired directly by formula derivation method and solved through LU-SGS iteration. The adjoint code is verified by comparing flux Jacobian and objective function gradient with finite differences. The design system is successfully applied to ONERA M6 wing transonic shape optimization design with the purpose of reducing drag, and the influence of volume constraint is also studied in this paper. It shows that the optimization method established is effective with a better application prospect.