An Adjoint Method for the Calculation of Non-Collocated Sensitivities in Supersonic Flow

This paper presents an adjoint method for the calculation of non-collocated sensitivities in supersonic flow. The goal is to develop a set of discrete adjoint equations and their corresponding boundary conditions in order to quantify the influence of geometry modifications on the pressure distribution at an arbitrary location within the domain of interest. First, this paper presents the complete formulation and discretization of the discrete adjoint equations. The special treatment of the adjoint boundary condition to obtain non-collocated sensitivities is also discussed. Second, we present results that demonstrate the application of the theory to a two-dimensional inverse design problem using the traditional Ni-bump geometry.