  Acoustic waves in a slightly compressible fluid saturating porous periodic
structure are studied using two complementary approaches: 1) the periodic
homogenization (PH) method provides effective model equations for a general
dynamic problem imposed in a bounded medium, 2) harmonic acoustic waves are
studied in an infinite medium using the Floquet-Bloch (FB) wave decomposition.
  In contrast with usual simplifications, the advection phenomenon of the
Navier-Stokes equations is accounted for. For this, an acoustic approximation
is applied to linearize the advection term. The homogenization results are
based the periodic unfolding method combined with the asymptotic expansion
technique providing a straight upscaling procedure which leads to the
macroscopic model defined in terms of the effective model parameters. These are
computed using the characteristic responses of the porous microstructure.
  Using the FB theory, we derive dispersion equations for the scaffolds
saturated by the inviscid, or the viscous, barotropic fluids, whereby the
advection due to a permanent flow in the porous structures is respected. A
computational study is performed for the numerical models obtained using the
finite element discretization. For the FB methods-based dispersion analysis,
quadratic eigenvalue problems must be solved. The numerical examples show
influences of the microstructure size and of the advection generating an
anisotropy of the acoustic waves dispersion.
