  Homogenization of a thin micro-structure yields effective jump conditions
that incorporate the geometrical features of the scatterers. These jump
conditions apply across a thin but nonzero thickness interface whose interior
is disregarded. This paper aims (i) to propose a numerical method able to
handle the jump conditions in order to simulate the homogenized problem in the
time domain, (ii) to inspect the validity of the homogenized problem when
compared to the real one. For this purpose, we adapt an immersed interface
method originally developed for standard jump conditions across a
zero-thickness interface. Doing so allows us to handle arbitrary-shaped
interfaces on a Cartesian grid with the same efficiency and accuracy of the
numerical scheme than those obtained in an homogeneous medium. Numerical
experiments are performed to test the properties of the numerical method and to
inspect the validity of the homogenization problem.
