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We study the motion of an ideal incompressible fluid in a perforated domain.The porous medium is composed of inclusions of size $a$ separated by distances$\tilde d$ and the fluid fills the exterior. We analyse the asymptotic behaviorof the fluid when $(a,\tilde d) \to (0,0)$.  If the inclusions are distributed on the unit square, this issue is studiedrecently when $\frac{\tilde d}a$ tends to zero or infinity, leaving aside thecritical case where the volume fraction of the porous medium is below itspossible maximal value but non-zero. In this paper, we provide the first resultin this regime. In contrast with former results, we obtain an Euler typeequation where a homogenized term appears in the elliptic problem relating thevelocity and the vorticity.  Our analysis is based on the so-called method of reflections whoseconvergence provides novel estimates on the solutions to the div-curl problemwhich is involved in the 2D-Euler equations.

A homogenized limit for the 2D Euler equations in a perforated domain