多孔介质瞬态分析中非分裂PML及时域有限元实现

周凤玺; 高贝贝

doi:10.3879/j.issn.1000-0887.2016.02.008

多孔介质瞬态分析中非分裂PML及时域有限元实现

doi: 10.3879/j.issn.1000-0887.2016.02.008

兰州理工大学土木工程学院, 兰州 730050

基金项目: 国家自然科学基金（11162008;51368038）;甘肃省环境保护厅基金(GSEP-2014-23);甘肃省教育厅研究生导师基金(1103-07)

详细信息

作者简介:
周凤玺（1979—），男，副教授，博士，博士生导师(通讯作者. E-mail: geolut@163.com).

中图分类号: O347.4
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出版历程
- 收稿日期: 2015-05-25
- 修回日期: 2015-09-30
- 刊出日期: 2016-02-15

A Non-Splitting PML for Transient Analysis of Poroelastic Media and Its Finite Element Implementation

School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, P.R.China

Funds: The National Natural Science Foundation of China(11162008;51368038)

摘要

摘要: 在波场的数值模拟中，完全匹配层(perfectly matched layer, PML)已经被证明是一种十分有效的吸收技术，并得到了广泛的应用.为了解决具有无限域的多孔介质中2阶弹性波动方程数值模拟中的吸收边界问题，提出了一种非分裂格式的PML(nonsplitting perfectly matched layer, NPML).首先，基于Biot多孔介质波动理论，建立了以固相和流相位移表示的2阶动力控制方程，其中考虑了固体颗粒和孔隙流体的可压缩性、惯性以及孔隙流体的粘性.其次，根据复伸展坐标变换的定义，通过Laplace变换获得了非分裂格式PML的频域表达式.然后，借助辅助函数将该方程变换到时间域内，得到了一种有效的非分裂PML.最后，基于Galerkin近似方法，给出了其时域有限元计算格式.通过数值算例分析了该非分裂格式的PML在饱和介质动力响应分析中的有效性.
- 非分裂完全匹配层 /
- 吸收边界 /
- Biot波动方程 /
- 有限元方法
Abstract: The perfectly matched layer (PML) absorbing boundary condition had been proved to be a highly effective absorption technique for the numerical simulation of wave propagation and therefore widely used. In order to solve the problems of absorbing boundary conditions in the numerical modeling of 2nd-order elastic wave equations for the infinite domain poroelastic media, a non-splitting perfectly matched layer (NPML) was proposed. Firstly, based on the theory of Biot’s wave equations and in view of the compressibility of solid particles and pore fluid, the inertia and the pore fluid viscosity, the 2nd-order dynamic governing equations were established in the form of solid and fluid displacements. Secondly, according to the complex coordinate stretching technique, the frequency domain formulations of the NPML were obtained by means of the Laplace transform. Afterwards, with the aid of auxiliary functions in the absorption layer, an effective NPML was built through the transform of the frequency domain formulations back to the time domain. Finally, the time domain finite element scheme of the NPML on the basis of Galerkin approximate method was provided. The effectiveness of the NPML in the dynamic response analysis of saturated poroelastic media is demonstrated with several numerical examples.
- non-splitting perfectly matched layer /
- absorbing boundary /
- Biot’s wave equation /
- finite element method

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参考文献(19)

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