Department of Mathematics, Florida State University
"Coupling and decoupling of flows in conduit and flows in porous media"
It is necessary to consider the coupling effect of flows in conduit and flows in porous media in certain applications such as flow and contaminant transport in karst aquifer. We discuss the derivation of the interface boundary conditions that are necessary to couple the flows, especially in the case of two-phase flows, using Onsager's extremum principle. We then consider numerical schemes that decouple the flows in conduit and those in porous media while preserving the energy law. The energy law guarantees the stability of the numerical scheme even for long-time simulations, a necessity for some physical applications.