We discuss our progress in upscaling physical models of flow with inertia and of coupled transport. The two scales of interest are porescale and mesoscale (lab scale). The flow models considered are Navier-Stokes at porescale and non-Darcy at mesoscale. The transport model describes advection of contaminant which may or may not undergo adsorption and reaction at porescale. The model is an example of a process for which the physical model at one scale does not quite match the physical model at the other scale. We outline analytical issues and computational techniques applied to solve this problem, and show some recent results; this is joint work with A. Trykozko (Univ. of Warsaw). In particular, we discuss a projection method used for correcting a non-conservative velocity field. We will also draw on related work in collaboration with K. Kennedy, and experimental results obtained by W. Sobieski and A. Trykozko.