In this work, the modeling and numerical resolution in the multidimensional framework of the interaction between the congested shallow water model and a polytropic air pocket dynamics are addressed. A weak coupling strategy is adopted and the air pocket connectivity is obtained by comparing there horizontal supports. Several numerical simulations illustrate the relevance of the model and the robustness of the numerical strategy. In particular, the method seems well suited to the numerical study of the hydraulics of underground rivers and coastal caves such as the Cosquer cave, and to the simulation of the marine energy converter such as the oscillating water column.