Abstract
This paper simulates wave propagation in an elastic medium containing elastic, fluid, rigid, and empty heterogeneities, which may be thin. It uses a coupling formulation between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS). The full domain is divided into subdomains, which are handled separately by the BEM/TBEM or the MFS, to overcome the specific limitations of each of these methods. The coupling is enforced by applying the prescribed boundary conditions at all medium interfaces. The accuracy, efficiency, and stability of the proposed algorithms are verified by comparing the results with reference solutions. The paper illustrates the computational efficiency of the proposed coupling formulation by computing the CPU time and the error. The transient analysis of wave propagation in the presence of a borehole driven in a cracked medium is used to illustrate the potential of the proposed coupling formulation.
Highlights
Various numerical methods have been proposed to simulate the propagation of waves in elastic and acoustic media, since analytical solutions are only known for simple and regular geometries e.g., 1–6
The paper extends that work with a formulation which couples the BEM/TBEM and the MFS to simulate the propagation of waves involving the fluid-solid interaction, as in the case of multielastic fluid layer systems, acoustic logging, and cross-hole surveying geophysical prospecting techniques 40, 41
The proposed coupling algorithms MFS/BEM and MFS/TBEM described are verified against BEM and MFS solutions by solving the elastic field produced by two circular inclusions embedded in an unbounded elastic medium, centred at 0.0 m, 20.0 m and 22.0 m, 5.0 m, with radii of 5.0 m and 6.0 m see Figure 3
Summary
Various numerical methods have been proposed to simulate the propagation of waves in elastic and acoustic media, since analytical solutions are only known for simple and regular geometries e.g., 1–6 These techniques include the thin-layer method TLM 7 , the boundary element method BEM 8 , the finite element method FEM 9, , the finite difference method FDM , the ray tracing technique , and the method of fundamental solutions MFS. The paper extends that work with a formulation which couples the BEM/TBEM and the MFS to simulate the propagation of waves involving the fluid-solid interaction, as in the case of multielastic fluid layer systems, acoustic logging, and cross-hole surveying geophysical prospecting techniques 40, 41. The applicability of the proposed method is shown by means of a numerical example that simulates the propagation of waves generated by a line blast load in the vicinity of a fluidfilled borehole driven in a cracked elastic medium
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