Abstract :

Many natural and engineering processes involve the interaction of free flow with flows in porous media. Well-known examples include flows in karst aquifers, PEM membrane, oil recovery, seawater intrusion, hyporheic flow, and almost all filtering processes. We present recent results in three important related areas: 1. How free flows couple with porous media flow? 2. Are there accurate numerical algorithms that decouple the free flow and the porous media flow? 3. When does the free flow and porous media flow decouple naturally?