In this paper we develop and study numerically a model to describe some aspects of soundpropagation in the human lung, considered as a deformable and viscoelastic porous medium(the parenchyma) with millions of alveoli filled with air. Transmission of sound throughthe lung above 1 kHz is known to be highly frequency-dependent. We pursue the key ideathat the viscoelastic parenchyma structure is highly heterogeneous on the small scaleε and use two-scale homogenization techniques to derive effectiveacoustic equations for asymptotically small ε. This process turns out tointroduce new memory effects. The effective material parameters are determined from thesolution of frequency-dependent micro-structure cell problems. We propose a numericalapproach to investigate the sound propagation in the homogenized parenchyma using aDiscontinuous Galerkin formulation. Numerical examples are presented.
