Emulation of sound reduction index measurement methods for sonic crystal noise barriers using periodic boundary conditions in FDTD

The acoustic performance of Sonic Crystal Noise Barriers (SCNBs) is strongly influenced by the angle-dependent nature of their transmission behaviour, which challenges the interpretation of standardized measurement methods. The present work focuses on the numerical emulation of three assessment procedures: the diffuse-field method (EN 1793-2), the direct-field in situ method (EN 1793-6), and a horizontal-incidence approach proposed here to more realistically represent conditions near linear noise sources such as roads and railways. In order to reproduce these measurement scenarios with controlled precision, three finite-difference time-domain (FDTD) implementations of periodic boundary conditions (Multiple Unit Cells, Sine–Cosine, and Transformed Field) are examined and applied to both a homogeneous reference layer and a representative sonic crystal barrier. The findings indicate that the assumed incidence distribution exerts a substantial influence on the estimated insulation. The in situ normal-incidence method substantially overestimates the Transmission Loss in frequency ranges governed by Bragg scattering, while the diffuse-field and horizontal-incidence methods yield comparable and more realistic values. It is evident that, among the numerical techniques, the Transformed Field method provides the most efficient and accurate broadband tool for conducting these emulations over wide angular ranges. The study demonstrates that an efficient, angle-resolved numerical emulation of measurement methods is essential to avoid mischaracterizing the sound insulation of SCNBs and to bridge the gap between laboratory protocols and real-world acoustic exposure.