This paper presents a method to control the discretization error in multipoint aerodynamic shape optimization using output-based adapted meshes. The meshes are adapted via adjoint-based error estimates, taking into account both the objective and constraint output errors. A multi-fidelity optimization framework is then developed by taking advantage of the variable fidelity offered by adaptive meshes. The objective functional and its sensitivity at each design point (operating condition) are first evaluated on the same initial coarse mesh, which is then subsequently adapted for each design point individually as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. As the shape approaches the optimal design, the mesh at each design point becomes finer, in regions necessary for that particular operating condition. The multi-fidelity framework is tightly coupled with the objective error estimation to ensure the optimization accuracy at each fidelity. Computational savings arise from a reduction of the mesh size when the design is far from optimal and avoiding an exhaustive search on low-fidelity meshes. The proposed method is demonstrated on multipoint drag minimization problems of a transonic airfoil with lift and area constraints. Improved accuracy and efficiency are shown compared to traditional fixed-fidelity optimization with a fixed computational mesh.

本文提出了一种基于输出的自适应网格在多点空气动力学形状优化中控制离散误差的方法。网格通过基于伴随的误差估计进行调整，同时考虑了目标输出误差和约束输出误差。然后，利用自适应网格提供的可变保真度来开发多保真度优化框架。首先在相同的初始粗网格上评估每个设计点（操作条件）的目标功能及其灵敏度，然后随着形状优化的进行，分别针对每个设计点进行调整。设置优化的工作量很小，因为初始网格可能相当粗糙且易于生成。随着形状接近最佳设计，每个设计点处的网格都会变得更细，在特定操作条件所必需的区域中。多保真度框架与客观误差估计紧密结合，以确保每个保真度的优化精度。当设计远非最佳时，减小网格尺寸会节省计算成本，并且避免在低保真网格上进行详尽的搜索。在具有升力和面积约束的跨音速机翼的多点阻力最小化问题上证明了该方法。与具有固定计算网格的传统固定保真度优化相比，显示了更高的准确性和效率。当设计远非最佳时，减小网格尺寸会节省计算成本，并且避免在低保真网格上进行详尽的搜索。在具有升力和面积约束的跨音速机翼的多点阻力最小化问题上证明了该方法。与具有固定计算网格的传统固定保真度优化相比，显示了更高的准确性和效率。当设计远非最佳时，减小网格尺寸会节省计算成本，并且避免在低保真网格上进行详尽的搜索。在具有升力和面积约束的跨音速机翼的多点阻力最小化问题上证明了该方法。与具有固定计算网格的传统固定保真度优化相比，显示了更高的准确性和效率。