2.5D singular boundary method for exterior acoustic radiation and scattering problems

Abstract

In this paper, a numerical methodology based on a two-and-a-half-dimensional (2.5D) singular boundary method (SBM) to deal with acoustic radiation and scattering problems in the context of longitudinally invariant structures is proposed and studied. In the proposed 2.5D SBM, the desingularisation provided by the subtracting and adding-back technique is used to determine the origin intensity factors (OIFs). These OIFs are derived by means of the OIFs of the Laplace equation. The feasibility, validity and accuracy of the proposed method are demonstrated for three acoustic benchmark problems, in which detailed comparisons with analytical solutions, the 2.5D boundary element method (BEM) and the 2.5D method of fundamental solutions (MFS) are performed. As a novelty of the present study, it is found that the 2.5D SBM provides a higher numerical accuracy than the 2.5D linear-element BEM and lower than the 2.5D quadratic-element BEM. Although the results obtained depict that a nodal approximation of the boundary geometry leads to a significant reduction in the accuracy of the 2.5D SBM, the delivered errors are still acceptable. For complex geometries, the 2.5D SBM is found to be simpler and more robust than the 2.5D MFS, since no optimization procedure is required.