Reduction of the Adjoint Gradient Formula for Aerodynamic Shape Optimization Problems

We present a new continuous adjoint method for aerodynamic shape optimization using the Euler equations, which reduces the computational cost of the gradients by reducing the volume integral part of the adjoint gradient formula to a surface integral. The savings are particularly significant for three-dimensional aerodynamic shape-optimization problems on general unstructured and overset meshes. To validate the concept, the new gradient equations have been tested for various aerodynamic shape-optimization problems, including an inverse problem for three-dimensional wing configurations, and drag-minimization problems of a single-element airfoil and a three-dimensional wing-fuselage configuration