In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy, and post-Darcy. Because of their different natures, these are usually treated separately in the literature. To study complex flows ...

We describe a spectrally filtered discrete-in-time downscaling data assimilation algorithm and prove, in the context of the two-dimensional Navier-Stokes equations, that this algorithm works for a general class of interpolants, ...