Simplified analytical model for sound level prediction at shielded urban locations involving multiple diffraction and reflections.

Accurate and efficient prediction of the sound field in shadow zones behind obstacles is a challenging task but essential to produce urban noise maps. A simplified method is presented to predict sound levels at shielded urban locations, including multi-edge diffraction over successive buildings and multiple reflections between parallel façades. The model is essentially based on Pierce's diffraction theory, where the Fresnel Integral is approximated by trigonometric functions for efficient evaluation, and parameterized for urban environments. The model has been validated for idealized urban configurations by comparing to the results of Pierce's theory and a full-wave numerical method. In case of multi-edge diffraction over buildings in absence of a source or receiver canyon, deviations from the full-wave simulations are smaller than 2 dB for the octave bands with central frequencies ranging from 125 to 1000 Hz. However, larger errors are made when receivers are close to the extension line from the diffraction edge closest to the receiver. In case of combining the simplified multi-edge diffraction model with an efficient approach for including the series of mirror sources and mirror receivers, based on the Hurwitz-Lerch transcendent, this same accuracy is obtained.