  An adaptive model for the description of flows in highly heterogeneous porous
media is developed in~\cite{FP21,FP23}. There, depending on the magnitude of
the fluid's velocity, the constitutive law linking velocity and pressure
gradient is selected between two possible options, one better adapted to slow
motion and the other to fast motion. We propose here to validate further this
adaptive approach by means of more extensive numerical experiments, including a
three-dimensional case, as well as to use such approach to determine a
partition of the domain into slow- and fast-flow regions.
