Dr. Béatrice Rivière
Title: Discontinuous Galerkin Methods for Modeling Porous Media: Theory and Simulations
Discontinuous Galerkin methods have been exponentially used by the scientific community over the last twenty years, for solving a multitude of problems modeled by linear and nonlinear partial differential equations. Due to the lack of continuity constraints between the grid cells, discontinuous Galerkin methods have been shown to be very flexible; for instance, they easily handle local mesh refinement and high order of approximation. The factthat these methods are locally mass conservative makes them particularly suitable for the solution of flow and transport problems in porous media. These problems are of critical importance in many engineering applications such as groundwater flows, hydrocarbons production, and carbon dioxide sequestration. Thanks to the increase in computational resources, scientists are able to model complex multicomponent multiphase problems in heterogeneous and anisotropic porous media. In this talk, we review the class of interior penalty discontinuous Galerkin and the class of hybridizable discontinuous Galerkin methods for solving the miscible displacement, two-phase and three-phase flows problems in heterogeneous media. Accuracy and robustness of the numerical methods are demonstrated. Recent advances in the design of bound-preserving discontinuous Galerkin methods are also presented.