2.5D singular boundary method for acoustic wave propagation

Abstract

This study proposes a two-and-a-half-dimensional (2.5D) singular boundary method (SBM) to solve three dimensional (3D) acoustic problems with a constant cross section excited by harmonic point sources. The SBM expands the solution of a problem with a linear combination of fundamental solutions of the governing equation. The singular terms in the fundamental solutions are replaced by the origin intensity factors (OIFs). Nevertheless, the SBM suffers quadratically increasing memory consumption and operation count with respect to the degree of freedoms owing to the fully-populated coefficient matrices. This makes the SBM not applicable in road and rail traffic systems, where the domain of interest always is a few hundred meters long. Taking advantage of the invariant cross section in these problems, the 2.5D method is devised to decompose the 3D problem into a summation of a set of simpler 2D problems, and thus enables the SBM to solve 3D traffic acoustic problems. To recast the results of 3D problems, a new formulation for numerical integration is proposed. The proposed 2.5D SBM is tested to two problems in both full-space and half-space to illustrate its effectiveness and feasibility.