  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.
