COSAM » Events » 2019 » September » DMS Colloquium: Beatrice Riviere

DMS Colloquium: Béatrice Rivière
Time: Sep 06, 2019 (04:00 PM)
Location: Parker Hall 250


Speaker: Béatrice Rivière, Rice University


Title: High order discontinuous Galerkin methods for solving the miscible displacement problem in porous media

Abstract: The accurate prediction of flow and transport in porous media is essential in optimizing the clean-up of contaminated groundwater or the production of hydrocarbons from oil reservoirs. In the miscible displacement problem, a solvent is injected and mixes with the resident fluid (contaminant or oil). The fluid mixture then propagates through the set of connected pores. At the Darcy scale, the mathematical model is a system of partial differential equations coupling flow and transport. This talk presents high order interior penalty discontinuous Galerkin (IPDG) methods and hybridizable discontinuous Galerkin (HDG) methods for solving the nonlinear system of equations. HDG methods retain the positive features of IPDG, but the number of globally coupled degrees of freedom for high order HDG is significantly smaller. The proposed numerical methods are shown to be accurate on coarse meshes when the polynomial degree increases. The numerical approximations of the solvent concentration exhibit sharp fronts even in highly heterogeneous media. Finally, the discontinuous Galerkin methods in space can accurately model viscous fingering. Viscous fingering in porous media may occur when a fluid with low viscosity is used to displace a fluid with high viscosity. For this type of flow instability, a tiny perturbation can be amplified exponentially, which triggers a finger-like pattern in the fluid concentration profile during the fluid displacement.  Simulations in two and in three dimensions show the growth and propagation of fingers for large mobility ratios and large Peclet numbers. Results are compared with those obtained by using a generic cell-centered finite volume method.


Short Bio-sketch
Béatrice Rivière is a Noah Harding Chair and Professor in the Department of Computational and Applied Mathematics at Rice University. She received her Ph.D. in 2000 from the University of Texas at Austin. Her other degrees include a Master in Mathematics in 1996 from Pennsylvania State University and an Engineering Diploma in 1995 from Ecole Centrale, France. She is the author of more than one hundred scientific publications in numerical analysis and scientific computation. Her book on the theory and implementation of discontinuous Galerkin methods is highly cited. Her research group is funded by the National Science Foundation, the oil and gas industry and the Gulf Coast Consortia for the Quantitative Biomedical Sciences.

Dr. Rivière has worked extensively of the development and analysis of numerical methods applied to problems in porous media and in fluid mechanics. Her current research deals with the development of high-order methods in time and in space for multiphase multicomponent flows (in rigid and deformable media); the modeling of pore scale flows for immiscible and miscible components; the numerical model of oxygen transport in a network of blood vessels; the analysis of PDE-based neural networks for image segmentation and the design of iterative solvers.

Dr. Rivière is an associate editor for the SIAM Journal on Numerical Analysis, for the SIAM Journal on Scientific Computing, for Results in Applied Mathematics, and a member of the editorial board for Advances in Water Resources. She has graduated a total of fourteen Ph.D. students, with eight working in academia and five in industry.


Faculty host: Thi-Thao-Phuong Hoang

Last updated: 08/22/2019