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在无限域波动模拟中引入透射边界条件时,目前多将边界上的透射公式与内域的有限元法结合使用,其计算精度由有限元方法决定,而谱元法因结合有限元和频谱法的优势则比有限元空间域积分具有更高的计算精度。该文基于谱元法非等距网格划分特性,研究了内域的谱元法与边界上的透射公式结合的理论方法,给出了相应的透射公式使用方法,并基于建立的谱元法波动数值模型探讨了透射公式的稳定性问题。研究表明:空间域插值系数需控制在一个合理范围内,空间域插值方法相对于时间域插值方法更为稳定,高频失稳出现可能性相对较小;Gamma算子的使用可提高模拟的精度,采用Gamma算子后对于高阶透射公式仍可出现低频漂移现象,可结合降阶消漂的方式实现稳定精度高的透射边界应用。
When introducing the boundary conditions of wave propagation in the infinite domain, the transmission formulas on the boundary are combined with the finite element method in the inner domain. The calculation accuracy is determined by the finite element method. However, the combination of the element method and the finite element method The advantage is higher than the finite element space domain integral calculation accuracy. Based on the characteristics of non-equidistant grids by spectral element method, this paper studies the theoretical method combining spectral method in the inner domain with the transmission formula on the boundary and gives the corresponding method of using the transmission formula. Based on the established spectral element method The wave numerical model discusses the stability of the transmission formula. The results show that the spatial domain interpolation coefficients need to be controlled within a reasonable range, the spatial domain interpolation method is more stable than the time domain interpolation method, and the possibility of high frequency instability appears relatively small. The use of Gamma operator can improve the simulation accuracy , The use of Gamma operator for high-order transmission formula can still occur low-frequency drift phenomenon can be combined with reduced-order de-floating method to achieve high precision and stability of the transmission boundary applications.