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Acoustic waves in a slightly compressible fluid saturating porous periodicstructure are studied using two complementary approaches: 1) the periodichomogenization (PH) method provides effective model equations for a generaldynamic problem imposed in a bounded medium, 2) harmonic acoustic waves arestudied in an infinite medium using the Floquet-Bloch (FB) wave decomposition.  In contrast with usual simplifications, the advection phenomenon of theNavier-Stokes equations is accounted for. For this, an acoustic approximationis applied to linearize the advection term. The homogenization results arebased the periodic unfolding method combined with the asymptotic expansiontechnique providing a straight upscaling procedure which leads to themacroscopic model defined in terms of the effective model parameters. These arecomputed using the characteristic responses of the porous microstructure.  Using the FB theory, we derive dispersion equations for the scaffoldssaturated by the inviscid, or the viscous, barotropic fluids, whereby theadvection due to a permanent flow in the porous structures is respected. Acomputational study is performed for the numerical models obtained using thefinite element discretization. For the FB methods-based dispersion analysis,quadratic eigenvalue problems must be solved. The numerical examples showinfluences of the microstructure size and of the advection generating ananisotropy of the acoustic waves dispersion.

Modelling wave dispersion in fluid saturating periodic scaffolds