中文摘要：

声传播算子（AWP）将空间微分计算的谱方法和时域积分计算的切比雪夫展式法结合，是一种高效的声场时域计算方法，该方法是分析声场时域演化的有效工具．现有的声传播算子的计算方法并不包含任何声源，这约束了其应用范围，只能考察给定初始声场分布的声学演化过程．本文从含有声源的声波方程解析解出发，探讨声传播算子中引入声源的计算方法，对于简谐声源，声源对声场分布的贡献仍然可以用谱方法和切比雪夫展式的组合形式加以实现，且算法的改动并未带来运算量的显著提升，并且计算精度也得到了保证．高斯平滑截取窗作为吸收边界条件来消除由计算边界产生的伪反射波，以此来模仿无界自由声场．同时研究表明，同无源声传播算子方法的计算特性一致，含源声传播算子方法中高采样点声场空间的仿真结果同理论值之间的误差更小．

英文摘要：

Acoustical Wave Propagator （AWP） is an efficient time domain calculation method, which combines the spectral method in frequency domain and the Chebyshev expansion method in time domain. Currently, AWP does not include any sound source, which limits its application only in investigating the acoustic wave evolution with the specific initial sound field distribution. In this paper, the sound source is introduced in AWP with some proper modifications. For sinusoidal sound source, the contribution of the source to the sound field can be calculated by the spectral method and Chebyshev expansion efficiently. The modification of AWP results in a satisfactory computational accuracy with only a limited increase of the computational burden. Gaussian smoothing is applied asthe absorbing boundary condition to eliminate the spurious reflection caused by the computational boundary, which can simulate a free acoustical field. Also, as AWP without sound source, it is proved that the high sampling points in the computational field will lead a high accuracy. Several examples are shown to verify the high accuracy of the simulating results of AWP with the sound source and the efficiency of the Gaussian smoothing method. The relative error of the sound pressure calculation result can be restricted within 1 × 10^-5 in most of the acoustical field.