Beatrice Riviere, Rice University – Applied Mathematics Colloquium

Title: Numerical methods for porous media flows at the pore scale and Darcy scale

Abstract: Modeling multicomponent flows in porous media is important for many applications relevant to energy and environment. In the first part of the talk, I will present a pore-scale flow model based on the coupling of Cahn-Hilliard and Navier-Stokes equations. At the micro-meter scale, the rock structure is given and the fluid flows through the connected pores. In the second part of the talk, I will discuss a Darcy-scale flow model, that assumes the existence of a representative elementary volume and that utilizes averaged quantities such as permeability and porosity.  The numerical discretization in space is the interior penalty discontinuous Galerkin methods of arbitrary order. Convergence of the algorithm is guaranteed by a theoretical analysis. Numerical studies of wettability at the pore-scale and viscous fingering at the Darcy scale show the robustness and accuracy of the methods.