音爆的精确模拟对于超声速客机的低音爆研究与设计意义重大。由于计算能力的限制，客机巡航高度的音爆全场直接模拟目前还难以实现。现有的音爆预测方法一般分为两步，先通过超声速线化理论或计算流体力学的方法得到音爆近场的过压值（Over-pressure）分布，再通过声学理论将近场声压信号推进至远场，以获得飞行器的地面音爆信号。在远场计算中，传统的波形参数法没有考虑音爆传播过程中的经典吸收和分子驰豫效应所造成的声能损失，得到的激波没有厚度，导致计算得到的远场声压级不准确。基于算子分裂法，开展了非线性声学中的增广Burgers方程的数值解法研究。通过计算第二届音爆预测研讨会（SBPW-2）发布的两个标准算例，验证了该方法可以实现地面音爆波形的精确预测。发现在近场声压信号前加入一段无幅值的缓冲信号可以有效提升"N"波上升时间的模拟精度。网格收敛性研究表明适当加密计算网格是有必要的。在此基础上研究了大气声吸收对地面波形的影响，发现分子驰豫效应的影响要强于经典吸收。最后，研究了不同湿度、温度对地面音爆波形的影响，发现干燥、低温的环境对音爆信号的过压值有抑制作用。
Accurate simulation of sonic boom is of great importance for the study of low-boom design. It is hard to conduct direct full-field simulation of sonic boom at the cruising altitude of supersonic aircraft due to limitation of computing capacity. Current methods for sonic boom prediction usually have two steps. Firstly, the near field over-pressure is obtained according to the supersonic linearized theory or computational fluid dynamics. Then the near field signal is advanced to the far field using acoustic methods to get the ground pressure signature of aircraft. During the calculation of the far field, the traditional waveform parameter method does not take into consideration the loss of sound energy resulting from classical attenuation or molecular relaxation effect in propagation, so that the final shock waves obtained do not have thickness, making the far field sound pressure level inaccurate. This paper, based on the splitting method, investigates the numerical methods of the augmented Burgers equation in nonlinear acoustics. Two standard numerical examples published in the SBPW-2 are calculated, verifying that the method proposed can accurately predict the ground signature. It can be found that adding a zero-amplitude buffer signal to the near field signal is very effective to improve the simulation accuracy in the rising of ‘N’ wave. A study of mesh convergence demonstrates that it is useful to refine the grid density properly. A study of atmospheric sound absorption finds that the effect of relaxation effect is stronger than classical attenuation. Dry and cold atmosphere is found to have adverse effect on over-pressure of sonic boom signal based on an analysis of influence of humidity and temperature on ground pressure signature.
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