  The present work deals with the resolution of the Linearized Navier-Stokes
problem in a domain made of an array that consists into a repetition of
elongated resonators connected to an half-space. We provide and justify a limit
equivalent model which takes into account the presence of resonators array as
an equivalent boundary condition. Our approach combines the method of matched
asymptotic expansions and the method of periodic surface homogenization adapted
to more than two scales, and a complete justification is included in the paper.
