本文推导了声波方程频散函数,分析了伪谱法的空间网格大小和采样周期对数值频散的影响,通过数值模拟实验得到了最佳空间参数选择方法.结果表明:伪谱方法稳定数值模拟的最大空间采样间距选取原则是使中波长(奈奎斯特频率的一半)的采样点数为2个;对于所有维度,稳定性随空间采样间距的增加而增加,但不易变化太大,变化太大时需要适当减小震源子波的主频,以满足空间合理采样;空间采样间距的大小设置,需要考虑满足采样定理和稳定性计算条件,并且稳定性条件对空间采样间距的要求更加严格;伪谱法数值模拟的最佳(数值频散最小)空间参数选择为中波长2个采样点,对应主波长约6～7个采样点.以上研究对于采用伪谱法进行声波方程数值模拟过程中,如何合理选择模拟参数提供一些参考.%The dispersion function of acoustic wave equation for pseudo-spectral algorithm is derived.And,selection principle of the spatial sampling space for the pseudo spectral method and the influence of the spatial sampling interval and the time sampling period on the numerical dispersion are analyzed.Numerical experiments indicates that the selection principle of the spatial sampling space for stable numerical simulation is that the sampling points of the medium wavelength which frequency is half of Nyquist-frequency is 2;for all dimensions,the stability increases with the increase of the space sampling space,but the increment can not be too large;when setting the value of the space sampling interval,it is needed to consider the sampling theorem of the time domain and the stability condition,and the stability condition is more strict to the grid size;the optimal(smaller numerical dispersion) spatial grid number for the numerical simulation of pseudo spectral method is 2 sampling points for the medium wavelength,corresponding to about 6～7 sampling points for the main wavelength.The above research provides some reference for how to select the reasonable simulation parameters using pseudo spectral method.
展开▼
