In this work, a computational homogenization framework is proposed to model flows in domains containing very small obstacles. On the one hand, this problem is well-known and it can be easily solved using Darcy’s law where the fine scale heterogeneity due to the obstacles is represented at the coarse scale of the domain through the so-called permeability tensor. On the other hand, Darcy’s law no longer applies for inertial flows. The proposed framework relies on a separation between the flow at the coarse scale of the domain and the flow at the fine scale of the obstacles but both scales are solved simultaneously with a two-way coupling. This approach is an extension of a homogenization theory recently proposed for the steady case where, as opposed to Darcy’s law, both the fine and coarse scale problems are of Stokes type. This eases the extension to the unsteady case and the implementation of this theory as an FExFE or FE² framework where fine scale meshes containing the obstacles are attached at each integration point of the coarse scale mesh. At each time step, a nonlinear fully coupled problem is formulated and solved to compute the solution at both scales. Several challenging aspects of this framework are addressed in this work, including the incompressibility constraint and the Newton-Raphson procedure at both scales. This framework is implemented in the FEMS open-source software.