The research agenda of this project are: (1) Modeling of preferential transport from mesoscale to macroscale; (2) Modeling of fast flow in narrow fractures in porous media; (3) Pseudo-parabolic Models of Dynamic Capillary Pressure; (4) Adaptive computational upscaling of flow with inertia from porescale to mesoscale; (5) Adaptive modeling of nonlinear coupled systems; and (6) Adaptive modeling and a-posteriori estimators for coupled systems with heterogeneous data.