卷积完全匹配层在二维声波吸收流体介质中的有限元计算

Convolution perfectly matched layer introduced in FE calculation of 2D acoustic wave in absorptive fluid media

将基于复坐标变换和复频移扩展坐标变量的卷积完全匹配层Convolution Perfectly Matched Layer(CPML)引入到二维吸收流体介质声波方程的有限元(FEM)计算中,其作为一种吸收边界条件应用在了数值计算的边界截断上。与传统的PML相比,CPML的优势在于它不需要把场方程分裂开,使待求解方程的数目减少,并使其具有更好的稳定性和更高的吸收性能。文中给出了二维吸收声波的频域和时域CPML方程,并在有限元计算软件COMSOL中完成数值计算。结果表明,CPML边界层能有效吸收损耗流体介质中的声波,能有效衰减了进入其中的声场能量。

A method was presented to introduce convolution perfectly matched layer（CPML）,based on complex coordinate transformation and complex frequency shifted stretched-coordinate matrices,into finite element calculation of 2D acoustic wave equation in absorptive fluid media.The main advantage of CPML over the traditional PML was that it did not need to split wave field,it reduced the number of equation and led to better stability and effective absorption.Here,CPML equations were deduced in frequency domain and in time domain,respectively and the calculations were done with the FE software COMSOL.The results of numerical simulation in time domain demonstrated that CPML absorbs effectively outgoing energy of absorptive fluid media.