Numerical solution of the Stokes-Brinkman model for porous media flows

Abstract

In porous media flows, specially those arising from petroleum exploration, the Darcy model is largely employed, which is suitable when the domain scale is much larger than the pore scale structure of the porous material. When free channels or high-porosity media are considered (such as fractures in the porous material, for instance), the Stokes-Brinkman model is more adequate, as an intermediate model between Darcy and direct solution in the pore scale modelled by the Stokes equations. This research proposal is concerned about the numerical solution of the Stokes-Brinkman modeling porous media flow. We intend to investigate the limits of this formulation, the numerical challenges in its discretization, as well as its viability for large scale simulations by using modern multiscale domain decomposition methods.