Directional reflection modeling via wavenumber-domain reflection coefficient for 3D acoustic field simulation

TL;DR

This paper introduces a 3D acoustic reflection modeling framework using wavenumber-domain reflection coefficients, enabling efficient simulation of direction-dependent reflections without explicit interior modeling, applicable to complex environments.

Contribution

The study extends a 2D reflection coefficient framework to 3D, allowing realistic simulation of direction-dependent acoustic reflections with reduced computational cost.

Findings

Accurate 3D simulation of direction-dependent reflections demonstrated.

Framework compatible with measured data and empirical models.

Reduces computational complexity compared to traditional methods.

Abstract

This study proposes a framework for incorporating wavenumber-domain acoustic reflection coefficients into sound field analysis to characterize direction-dependent material reflection and scattering phenomena. The reflection coefficient is defined as the amplitude ratio between incident and reflected waves for each propagation direction and is estimated from spatial Fourier transforms of the incident and reflected sound fields. The resulting wavenumber-domain reflection coefficients are converted into an acoustic admittance representation that is directly compatible with numerical methods such as the Boundary Element Method (BEM), enabling simulation of reflections beyond simple specular components. Unlike conventional extended reaction models, the proposed approach avoids explicit modeling of the material interior. This significantly reduces computational cost while allowing direct use of measured data, empirical models, or user-defined directional reflection characteristics. The validity of the proposed formulation was previously demonstrated by the authors through two-dimensional sound field simulations, in which accurate reproduction of direction-dependent reflection behavior was confirmed. In the present work, the framework is extended to three-dimensional analysis, demonstrating its applicability to more realistic and complex acoustic environments. The proposed approach provides a practical and flexible tool for simulating direction-dependent acoustic reflections and scattering, with potential applications in architectural acoustics, material characterization, and noise control.