Calculation of Aerodynamic Surface Sensitivities Using the Adjoint Method in a Subsonic/Supersonic Panel Code

An aircraft’s shape has a direct impact on the lift and drag it produces. In the early stages of designing an aircraft on a computer, engineers work to improve aircraft performance and efficiency by considering various shapes and configurations. Engineers use computer programs to analyze different designs and predict how each would perform in real-world conditions. Once an approximate aircraft shape is selected, adjustments to the shape can further improve the aircraft’s lift and drag characteristics. Engineers calculate a set of values called sensitivities that indicate which parts of the geometry should be changed to increase lift or reduce drag. A common numerical method known as a finite-difference method can be used to approximate the sensitivities. Although straightforward to implement, finite-difference calculations may take days and the results are limited in accuracy. A more efficient alternative, known as the adjoint method, calculates exact sensitivities in a fraction of the time required by finite differences. This work derives the equations needed to apply the adjoint method to supersonic aerodynamic analysis code. The implementation of the method is described and the resulting sensitivity values are validated. The adjoint method quickly produces accurate sensitivities for shapes in both subsonic and supersonic flow, as demonstrated through validation with the finite-difference method.