A novel hybrid SBM-MFS methodology for acoustic wave propagation problems

Abstract

In this paper, a novel hybrid meshless approach that combines the singular boundary method (SBM) and the method of fundamental solutions (MFS) to deal with two-dimensional (2D) exterior acoustic wave propagation problems is proposed and studied. The methodology is particularly devised to solve problems with complex boundary geometries containing geometric singularities such as corners and sharp edges. It employs the SBM to model intricate segments of these geometries and the MFS for the smooth ones. The proposed hybrid SBM-MFS method is studied in a 2D context in the framework of three benchmark examples involving acoustic radiation problems of circular-, square- and L-shaped objects in a full-space acoustic medium. In addition, the applicability of the proposed hybrid SBM-MFS methodology to predict the acoustic performance of a T-shaped thin barrier is also investigated. These examples are specifically designed to assess the feasibility, validity and accuracy of the hybrid SBM-MFS approach in comparison with the available analytical solutions and alternative numerical strategies such as the MFS, the SBM and the boundary element method (BEM). Numerical simulations demonstrate that the proposed method can match the level of accuracy of the MFS while keeps the robustness of the SBM when dealing with complex geometries, overcoming one the most important drawbacks of the traditional MFS. Moreover, the proposed hybrid SBM-MFS naturally avoids the non-uniqueness problem arising at the fictitious eigenfrequencies associated with the corresponding interior problems, a feature that neither the SBM nor the BEM inherently possesses.