Multiple Scattering and Visco-Thermal Effects on 2D Phononic Crystal

In this paper, we are interested in the transition between regimes here either visco-thermal or multiple scattering effects dominate for the propagation of acoustic waves through a 2D regular square array of rigid cylinders embedded in air. An extension of the numerical method using Schl\"omilch series is performed in order to account for visco-thermal losses. Comparison withexperimental data and results from classical homogenization theory allows to study the transition between a low frequency limit (where viscous and thermal effects dominate) and a high frequency regime (where multiple scattering effects become predominant). For this particular geometry, a large frequency domain where visco-thermal and multiple scattering effects coexist is found.