柱坐标系下浅海传播声场时域有限差分预报方法

Acoustic propagation field prediction in shallow water by using finite-difference time-domain method in a cylindrical coordinate system

直角坐标系下的时域有限差分方法在水声传播仿真时由于计算量太大而较少应用。文章利用时域有限差分方法推导了柱坐标系下的声波方程的近似表达式,结合复频移完全匹配层建立浅海声传播模型,在减少计算量的同时准确预报了传播信号声压的时域波形、传播声场的时空演变过程以及频域传播损失曲线。在柱坐标系下使用时域有限差分方法仿真Pekeris传播环境声场并与简正波和波数积分模型进行对比,分析了时域有限差分水声传播模型的适用范围。结果表明,时域有限差分方法仿真浅海中近程传播声场精度较高。模型的稳定性与时间和空间网格大小有关,声源频率越高,空间和时间网格划分越小,计算量越大。数值离散带来的频散误差累积会导致远场传播声场计算不准确,因此时域有限差分水声传播模型更适用于低频中近程声场计算。

Owing to the large amount of computation,the finite-difference method in time-domain is rarely applied to simulating underwater acoustic propagation in a Cartesian coordinate system.In this paper,the finite-difference timedomain method is used to derive an approximate expression of acoustic wave equation in a cylindrical coordinate system,and then by combining it with complex frequency shifted perfectly matched layers,a shallow water acoustic propagation model is constructed.The model reduces the amount of calculation and can accurately predicts the propagating signal waveforms and evolution process of the acoustic propagating fields in time domain and the transmission loss curves in frequency domain.Acoustic fields of Pekeris waveguide in shallow water are simulated by the finite-difference time-domain model in a cylindrical coordinate system.The scope of application of the model is analyzed by comparing normal mode model and wavenumber integration model.Results show that the proposed finitedifference time-domain method is highly accurate for short-range and medium range acoustic field prediction in shallow water.The stability of the model depends on the discrete spatial and time grid steps.For higher frequency of source,the space and time grid steps need to be smaller,which increase the amount of calculation.The accumulation of dispersion error of the model yields inaccurate acoustic field at long range.The research results show that the finitedifference time-domain model is more applicable to predict low-frequency short-range and medium range propagation field in shallow water.