Transport in Porous Media

The enormous growth in computational capabilities of recent years has made Navier–Stokes-based simulation of flow and transport in natural porous media possible. Because of the complex multiscale nature of porous media, however, full Navier–Stokes representation of the physics everywhere in the domain is not always feasible. Here, we employ, a filtering—or micro-continuum—approach to model the smallest length scales. The Darcy–Brinkman–Stokes (DBS) equation offers an appealing framework for this hybrid modeling. A general modeling framework based on the DBS equation is proposed. The approach is then used to bridge the gap between scales for several challenging problems, including flow in fractured media, pore-scale simulation with immersed boundary conditions, modeling of dissolution phenomena, and thermal evolution of oil shale.