辅助微分方程完全匹配层在声波方程数值模拟中的应用

摘要

在地震波数值模拟中，为提高算法精度，需要使用高阶时间更新格式，而普通的非分裂完全匹配层（PML）吸收边界局限于低阶时间格式。辅助微分方程完全匹配层（ADE-PML）是一种可以适应任意阶时间格式的非分裂完全匹配层技术，且可以直接应用复频移拉伸算子以提高 PML 在高角度入射时的效果。作者将 ADE-PML 应用于声波方程四阶 Runge-Kutta 时间格式的数值模拟中，对其吸收效能进行了检验。数值模拟表明，复频移 ADE-PML 在高角度入射时表现优于非复频移 ADE-PML。另外，不同辅助变量更新格式的吸收效果存在微小差异，显格式下计算结果与解析解吻合较好。长时间能量衰减计算表明ADE-PML 可以稳定至2×105时间步。%In seismic wave modeling,a high-order time marching scheme is required in order to increase the accuracy of the algorithm. However,ordinary unsplit perfectly matched layer (PML) absorbing boundaries are constrained to low-order time schemes.The auxiliary differential equation PML (ADE-PML)is a kind of unsplit PMLs that can be applied to arbitrary-order time schemes,and also can implement complex-frequency-shifted (CFS)coordinate tensor to enhance the performance of PML at high-angle incidence.We introduce the ADE-PML in the numerical modeling in fourth-order Runge-order time scheme for acoustic wave equations, and validate the efficiency. The numerical experiments demonstrate that CFS ADE-PML preforms better than non-CFS ADE-PML at high-angle incidence.Besides,there are minor distinctions among the absorbing efficiency of different update schemes for auxiliary variable,and the solution calculated by explicit scheme better agree with the analytical one.The long-time computation of energy decay shows that ADE-PML is stable up to 2 × 10 5 steps.