A transient boundary element method model of Schroeder diffuser scattering using well mouth impedance

Room acoustic diffusers can be used to treat critical listening environments to improve sound quality. One popular class is Schroeder diffusers, which comprise wells of varying depth separated by thin fins. This paper concerns a new approach to enable the modelling of these complex surfaces in the time domain. Mostly, diffuser scattering is predicted using steady-state, single frequency methods. A popular approach is to use a frequency domain Boundary Element Method (BEM) model of a box containing the diffuser, where the mouth of each well is replaced by a compliant surface with appropriate surface impedance. The best way of representing compliant surfaces in time domain prediction models, such as the transient BEM is, however, currently unresolved. A representation based on surface impedance yields convolution kernels which involve future sound, so is not compatible with the current generation of time-marching transient BEM solvers. Consequently, this paper proposes the use of a surface reflection kernel for modelling well behaviour and this is tested in a time domain BEM implementation. The new algorithm is verified on two surfaces including a Schroeder diffuser model and accurate results are obtained. It is hoped that this representation may be extended to arbitrary compliant locally reacting materials

Acquisition of bi-directional reflectance functions by Nearfield Acoustical Holography – a preliminary study

It is well known that material absorption and scattering is dependent on incidence and observation angle. Despite this, the corresponding standardised coefficients, which are used to represent these mechanisms within computational acoustic models, aggregate all such dependency into single random-incidence parameters. This limits the accuracy that can be achieved with computational acoustic models – even if these algorithms were to capture the wave physics perfectly, which they often do not, the results would not match physical reality because the input data is too low resolution. Bi-Directional Reflectance Functions are an established way of describing boundary absorption and scattering in computer graphics that have been suggested for use in acoustics. To date, several algorithms have been published that do or could use these in simulation, but no measurement methods are available to acquire them. There is also ambiguity over some aspects of their definition e.g. whether finite panel size is included as a scattering mechanism. This paper adopts a definition suitable for high-frequency Boundary Element Method algorithms that use oscillatory basis functions to capture wave directions. It then proposes an acquisition method based on double-layer Near-Field Acoustical Holography and assesses it accuracy using 2D simulations