Many physical, biological and engineering processes involve the coupling of free flows with flows in porous media. Well-known examples include filtration processes, flows in karstic geometry, hyporheic flow, and PEM fuel cell among many others.
We focus on three interrelated important issues associated with the coupled system: (1) physically relevant interface boundary conditions that couple the free flow and the porous media flow; (2) accurate numerical schemes that are able to decouple the two sub-systems so that legacy codes can be utilized to efficiently simulate the long-time transport phenomena; and (3) physically important parameter regimes where the system can be reduced to decoupled effective systems. Analytically, numerical and experimental tools will be employed to demonstrate several recent results in these directions.