ZHOU Feng-xi, GAO Bei-bei. A Non-Splitting PML for Transient Analysis of Poroelastic Media and Its Finite Element Implementation[J]. Applied Mathematics and Mechanics, 2016, 37(2): 195-209. doi: 10.3879/j.issn.1000-0887.2016.02.008
Citation: ZHOU Feng-xi, GAO Bei-bei. A Non-Splitting PML for Transient Analysis of Poroelastic Media and Its Finite Element Implementation[J]. Applied Mathematics and Mechanics, 2016, 37(2): 195-209. doi: 10.3879/j.issn.1000-0887.2016.02.008

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

doi: 10.3879/j.issn.1000-0887.2016.02.008
Funds:  The National Natural Science Foundation of China(11162008;51368038)
  • Received Date: 2015-05-25
  • Rev Recd Date: 2015-09-30
  • Publish Date: 2016-02-15
  • 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.
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