基于逆向增广 Burgers 方程的声爆反演技术

Sonic boom has always been one of the obstacles restricting the development of supersonic airliners. Hence，the low sonic boom design technology is particularly important in the design of supersonic airliners. The inverse augmented Burgers equation can invert the mid-field sound pressure signal to the near-field and provide optimization objectives for the low sonic boom inverse design. This study uses the operator splitting technique and the pseudoparabolic equation method to numerically solve the inverse Burgers equation and calculate the corresponding reversed equivalent-area. With the assistance of the three standard examples，we investigate the convergence of the numerical method，the accuracy of the solution，and the calculation accuracy of the inversion technique at different field heights and different rolling angles. Based on the characteristics of the inverse augmented Burgers equation，the feasibility of setting target waveforms in the mid-field for the inverse design method is discussed，and the propagation characteristics of high-frequency components in the sound pressure signal are studied. The research shows that the above method can accurately complete the inversion calculation of the sound pressure signal from the mid-field to near-field，and that using mid-field target waveforms instead of ground target waveforms can reduce the influence of the inversion distance on the inversion calculation process.