On mesh sensitivities and boundary formulas for discrete adjoint-based gradients in inviscid aerodynamic shape optimization

This paper shows how to obtain boundary formulas for discrete-adjoint-based sensitivities in shape optimization problems. The analysis is carried out for inviscid flows in two-dimensional, unstructured triangular grids. The new formulation agrees with known continuous adjoint boundary formulas for the sensitivities, and the derivation sheds light into the required approximations and the reasons for the equivalence (or lack thereof) between boundary and domain-based adjoint sensitivities. Alternative approximations are also discussed.