Multi-Domain Boundary Element Method for Sound Fields in and around Porous Absorbers

摘要

A multi-domain boundary element method for the calculation of sound fields in and around porous absorbers having a rigid frame is presented. Using the fact that the sound propagation in such absorbers can be described us if it would be an equivalent lossy fluid, the Kirchhoff-Helmholtz integral equation is applied. Consequently, an arbitrary configuration of porous absorbers and surrounding air space is treated as several acoustic domains with different wave numbers and impedances bounded together. A boundary element discretisation is applied to each of the domains. Afterwards, collocation leads to a system of linear equations. These equations may be solved to get both the sound pressure and its normal derivative at the boundaries. The method is implemented in 2D in a MATLAB code. The sound field generated by a plane wave incident on a cylinder of porous absorber material is used as a first benchmark. Results are compared to those of an analytical method using series of Hankel functions. The propagation of sound from a cylinder source above a finite depth absorber strip in a rigid baffle is calculated as a second example. Results of the method are compared to the results of a standard single domain boundary element method. The difference between the methods is discussed taking into account the extended and the local reaction of the absorber, respectively.