The alternating descent method applied to the control of the sonic boom

Nowadays, one of the main concerns in aeronautics research is related to the control and reduction of the noise generated by aircrafts. Indeed, one of the main goals in this broad and important area of industrial and commercial activity is to meet stringent noise and design constraints for supersonic airplanes [1]. In this goal, the sonic boom phenomenon produced by supersonic flights needs to be handled [3]. Currently, CFD techniques hardly compute the propagation of the supersonic shock wave from the near field of aircrafts to the ground level, to a distance of the order of 500 times the length of the plane. In this paper a numerical method will be developed for the simulation of the solution of the Augmented Burgers Equation that models this phenomenon [4]. The objective of the work is to capture accurately the arising quasi-shocks, as well as to mimic the large time behaviour of the solution. Besides, we consider an inverse problem consisting of, given a desired final state on a fixed time, obtaining the corresponding initial data for the pressure distribution in the near field of the plane. This will be analyzed as an optimal control problem, applying an adaptation of the alternating descent method presented in [2]. Numerical test will be performed to demonstrate the efficiency of the proposed approach, in comparison with the common adjoint methodology.