Discrete surprises in the computation of sensitivities from boundary integrals in the continuous adjoint approach to inviscid aerodynamic shape optimization

Abstract

The computation of flow sensitivities for shape optimization in flow problems using continuous adjoint-based boundary integrals reduces the computational costs and makes the scheme independent of the numerical solvers. However, certain analytic manipulations involved in the boundary formulation of the gradients do not hold valid at the discrete level near geometric singularities and lead to inconsistencies in the sensitivities, which add to already known mesh sensitivity issues at the same locations. Both questions appear to be relevant for inviscid flow problems only. These matters are examined and detailed numerical testing is performed on several conventional flow configurations.