Homogenization of the layer-structured dam problem with isotropic permeability

In this paper we address the homogenization of a free boundary model for a stratified porous dam problem. The motivation of the problem lies in the presence of a highly oscillating permeability to take into account the multilayer structure. Although several papers in the literature have partially studied this problem, we provide new additional results by using the periodic unfolding method. Furthermore, by using appropriate numerical techniques based on the combination of characteristics, duality and finite elements methods, several examples illustrate the here stated theoretical results and show the performance of the numerical methods.