二阶声场波动方程的非分裂完全匹配层算法

在声场仿真中,完全匹配层(Perfectly Matched Layer,PML)是一种十分有效的吸收边界并得到广泛应用。为了解决基于二阶声场波动方程数值仿真中的吸收边界问题,提出了一种非分裂PML算法。首先,基于伸缩坐标变换,推导了PML算法的频域表达式。然后,通过构造辅助微分方程,得到了非分裂PML的时域表达式。最后,进行了相关理论分析和数值仿真,结果表明:相对于已有的声场分裂PML算法,该算法在保持相同的吸收效率的同时,能较大地节约存储空间,提高计算效率,且更易于实现。

Unsplit perfectly matched layer for second-order acoustic wave equation

The Perfectly Matched Layer (PML) is an effective absorbing boundary and has been widely used in acoustic simulation. In order to develop an absorbing boundary condition for numerical simulation based on the second-order acoustic wave equation, an Unsplit PML algorithm is proposed. Firstly, frequency-domain expression of this method is formulated based on the complex stretching coordinate schema. Then, its time-domain expression is derived by formulating auxiliary differential equations. Finally, relative theoretical analysis and numerical simulation are carried out, the results of which demonstrate that compared with the existing Split PMLs, the proposed method has the same absorbing efficiency and can reduce storage greatly. It can also increase calculation efficiency with easier implementation.