拱形坑道建模及吸收边界性能比较

Design of vault tunnel model and comparison of the performance of absorbing boundary conditions

摘要:
建立了侧壁拱顶形坑道模型,该模型可根据实际需要在0～π／2范围内选择坑道的弧度. 将坑道看成有耗波导,采用TE10模和TM11模进行强迫激励,在此基础上比较了完全匹配层(Perfect Matched Layer, PML)、各向异性完全匹配层(Uniaxial PML, UPML)和卷积完全匹配层(Convolutional PML, CPML)三种在坑道计算模型中常用的吸收边界条件各方面的性能．数值结果表明：CPML边界条件可以有效吸收低频凋落模,克服了PML和UPML用于长时间计算造成的晚时反射,减小了计算域,缩短了计算时间．

Abstract:
An improved numerical model of the vaulted tunnel is proposed in this paper, which of the radian can be changed from zero to π／2. The tunnel can be seen as a waveguide approximately, and is excited by propagation model such as TE10, TE11, etc. In order to improve the effectiveness of the absorbing boundary condition(ABC), a perfectly matched layer (PML) medium with complex frequency-shifted(CFS) constitutive parameters is introduced for this study. The absorbing boundary is implemented by using the convolution PML (CPML), and the absorbing efficiency of CPML is compared with PML and UPML. Numerical results show that the CPML provides for a more efficient absorbing boundary than that of the PML and UPML at absorbing evanescent modes, and consequently the computation domain and computation time can be greatly reduced.