预测声屏障插入损失的抛物方程法及其初始声场研究

Study on the parabolic equation method and its starting field for predicting the insertion loss of sound barriers

Salomons建立的抛物方程（CNPE）方法可以预测非均匀环境中的声屏障插入损失。但是该方法在声屏障与声源距离较近时会产生较大误差。文中通过理论分析发现产生该问题的原因在于CNPE方法所使用的Gauss初始场仅适用于小仰角（10°以内）范围内的声波。为解决Gauss初始场引起的问题,推导了可以用于较大仰角声波的更高阶数的Gauss初始场。通过数值仿真对比了不同阶数的初始场在CNPE方法中的效果。结果表明：4阶初始场是最适合CNPE方法的初始场,将该初始场与CNPE方法相结合,可以准确预测当声屏障与声源距离较近时的插入损失.

The Crank-Nicholson parabolic equation （CNPE） method was used by Salomons to predict the insertion losses of sound barriers in inhomogeneous environments, however, the CNPE method will lead to large prediction errors when the sound source and the sound barrier is close to each other. It is found through theoretical analysis that the problem of the CNPE method is caused by the Gaussian starting field which is valid only for sound waves with small elevation angles （e.g., less than 10 degree）. To eliminate the restriction due to the starting field, the Gaussian starting field is re-derived and high order starting fields that are valid for large elevation angles are obtained. Numerical simulations are carried out to compare the performance of starting field of different order. The results show that the Gaussian starting field of 4th order is the most appropriate one for the CNPE method, and the CNPE method coupling with this starting field is able to predict the insertion loss accurately even if the sound source and the sound barrier is close to each other.