Application of the Adjoint Method to an Unstructured Subsonic/Supersonic Panel Method

Computational aerodynamic tools are commonly used to analyze discretized, rigid-body geometries and produce performance parameters such as lift and drag. The sensitivity of performance parameters to changes in surface geometry can guide adjustments that optimize aerodynamic performance. Numerical differentiation methods, such as finite-difference and complex-step, can estimate sensitivities, but these methods can be sensitive to step size and are computationally expensive for problems with many design variables. In contrast, the adjoint method provides an efficient analytical calculation of the sensitivity of performance parameters with respect to design variables, using a strategic ordering of operations. To the authors’ knowledge, this paper presents the first application of the adjoint method to an unstructured panel method for calculating surface sensitivities in subsonic and supersonic flows. Results show that application of the adjoint method allows for calculation of sensitivities in 1–5% of the time required by a finite-difference method.