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.
This paper models the propagation of sound in the vicinity of 3D acoustic barriers placed parallel to a building façade to mitigate the noise generated by point pressure sources. The barriers are assumed to be very thin rigid elements. The problem is solved by developing and implementing a 3D boundary element method formulation based on the normal derivative integral equation (TBEM). The TBEM is formulated in the frequency domain and the resulting hypersingular terms are computed analytically. After verifying the model against 2.5D BEM solutions, several numerical applications are described to illustrate the practical usefulness of the proposed approaches. Different longitudinal barrier geometries are simulated to evaluate the influence of this characteristic on the sound pressure level attenuation attained at the building façade. Keywords: acoustic wave propagation, 3D thin barriers, normal derivative integral equation, analytical integration of hypersingular integrals.
Sound wave propagation in 2D enclosed spaces containing a fluid-filled thin barrier is modelled in the frequency domain using a combination of three techniques: the boundary element method (BEM), the traction boundary element method (TBEM) and the method of fundamental solutions (MFS). In this formulation the body of the barrier is modelled with a mixed BEM/TBEM approach to cope with the thin body difficulty while the boundary of the host medium is modelled with an MFS technique. The MFS calculates the sound reflection from the boundary, as a linear combination of 2D virtual sources. These N virtual sources are located outside the domain on an imaginary boundary, to avoid singularities. The BEM/TBEM and MFS formulations are coupled by assuming that the absorption of the host medium boundary is obtained imposing an impedance boundary condition, while along the fluid-filled thin barrier boundary the continuity of pressure and pressure gradients is established.
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