A high-order absorbing boundary condition for scalar wave propagation simulation in viscoelastic multilayered medium

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lihua Wu ◽  
Mi Zhao ◽  
Xiuli Du
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Single Layer ◽  
High Order ◽  
Finite Domain ◽  
Scalar Wave ◽  
Infinite Domain ◽  
Multilayered Media ◽  
Absorbing Boundary ◽  
Content Type

Purpose The finite element method (FEM) is used to calculate the two-dimensional anti-plane dynamic response of structure embedded in D’Alembert viscoelastic multilayered soil on the rigid bedrock. This paper aims to research a time-domain absorbing boundary condition (ABC), which should be imposed on the truncation boundary of the finite domain to represent the dynamic interaction between the truncated infinite domain and the finite domain. Design/methodology/approach A high-order ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. A new operator separation method and the mode reduction are adopted to construct the time-domain ABC. Findings The derivation of the ABC is accurate for the single layer but less accurate for the multilayer. To achieve high accuracy, therefore, the distance from the truncation boundary to the region of interest can be zero for the single layer but need to be about 0.5 times of the total layer height of the infinite domain for the multilayer. Both single-layered and multilayered numerical examples verify that the accuracy of the ABC is almost the same for both cases of only using the modal number excited by dynamic load and using the full modal number of infinite domain. Using the ABC with reduced modes can not only reduce the computation cost but also be more friendly to the stability. Numerical examples demonstrate the superior properties of the proposed ABC with stability, high accuracy and remarkable coupling with the FEM. Originality/value A high-order time-domain ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. The proposed ABC is suitable for both linear elastic and D’Alembert viscoelastic media, and it can be coupled seamlessly with the FEM. A new operator separation method combining mode reduction is presented with better stability than the existing methods.

A stable high-order absorbing boundary based on continued fraction for scalar wave propagation in 2D and 3D unbounded layers

2019 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Huifang Li ◽  
Mi Zhao ◽  
Lihua Wu ◽  
Piguang Wang ◽  
Xiuli Du
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Continued Fraction ◽  
Coupled System ◽  
High Order ◽  
Scalar Wave ◽  
Absorbing Boundary ◽  
Content Type ◽  
High Order Time ◽  
2D And 3D

Purpose The purpose of this paper is to propose a stable high-order absorbing boundary condition (ABC) based on new continued fraction for scalar wave propagation in 2D and 3D unbounded layers. Design/methodology/approach The ABC is obtained based on continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient (DtN kernel) on the artificial boundary of a truncated infinite domain. The CF which has been used to the thin layer method in [69] will be applied to the DtN method to develop a time-domain high-order ABC for the transient scalar wave propagation in 2D. Furthermore, a new stable composite-CF is proposed in this study for 3D unbounded layers by nesting the above CF for 2D layer and another CF. Findings The ABS has been transformed from frequency to time domain by using the auxiliary variable technique. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the ABC-FEM coupled system is discussed and cured. Originality/value This manuscript establishes a stable high-order time-domain ABC for the scalar wave equation in 2D and 3D unbounded layers, which is based on the new continued fraction. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the coupled system is discussed and cured.

A 3D cylindrical PML/FDTD method for elastic waves in fluid‐filled pressurized boreholes in triaxially stressed formations

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1731-1743 ◽  
Author(s):  
Qing Huo Liu ◽  
Bikash K. Sinha
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Time Domain ◽  
Elastic Waves ◽  
Numerical Solutions ◽  
Fdtd Method ◽  
Uniaxial Stress ◽  
Absorbing Boundary Conditions ◽  
Principle Of Superposition ◽  
Absorbing Boundary

A new 3D cylindrical perfectly matched layer (PML) formulation is developed for elastic wave propagation in a pressurized borehole surrounded by a triaxially stressed solid formation. The linear elastic formation is altered by overburden and tectonic stresses that cause significant changes in the wave propagation characteristics in a borehole. The 3D cylindrical problem with both radial and azimuthal heterogeneities is suitable for numerical solutions of the wave equations by finite‐difference time‐domain (FDTD) and pseudospectral time‐domain (PSTD) methods. Compared to the previous 2.5D formulation with other absorbing boundary conditions, this 3D cylindrical PML formulation allows modeling of a borehole‐conformal, full 3D description of borehole elastic waves in a stress‐induced heterogeneous formation. We have developed an FDTD method using this PML as an absorbing boundary condition. In addition to the ability to solve full 3D problems, this method is found to be advantageous over the previously reported 2.5D finite‐difference formulation because a borehole can now be adequately simulated with fewer grid points. Results from the new FDTD technique confirm the principle of superposition of the influence of various stress components on both the borehole monopole and dipole dispersions. In addition, we confirm that the increase in shear‐wave velocity caused by a uniaxial stress applied in the propagation direction is the same as that applied parallel to the radial polarization direction.

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