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

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 4 th 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.