Aerodynamic Optimization through Automatic Differentiation and CFD

Automatic differentiation through source code transformation is a very powerful strategy for gradient-based optimization studies. However, memory allocation is a significant challenge if the transformed code is used without any modifications because automatic differentiation requires huge memory space. A general strategy to calculate derivatives of CFD solutions analytically through automatic differentiation without the memory problem is proposed in this paper. The problem of memory allocation is avoided by wisely modifying the code generated by automatic differentiation, and by feeding a set of converged solutions to the modified code. This strategy is validated by comparing derivatives computed through automatic differentiation and finite differentiation. The proof of concept application is the optimization of airfoil shape in transonic speed regime using a general CFD software available on line.