Beatrice Riviere 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 eighty 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. Riviere has worked extensively of the development and analysis of numerical methods applied to problems in porous media and in fluid mechanics. Dr. Riviere is an associate editor for the SIAM Journal on Numerical Analysis and a member of the editorial board for Advances in Water Resources. She has graduated a total of ten Ph.D. students, with five working in academia and five in industry.
Abstract: Thermodynamically based diffuse-interface methods are promising methods for direct pore-scale numerical simulations of multiphase multicomponent flows. The Cahn-Hilliard equations for a two-component flow are obtained after minimization of the total Helmholtz free energy. In this talk, we present a discontinuous Galerkin discretization of the coupled Cahn-Hilliard equations with the Navier-Stokes equations. Wettability on rock-fluid interfaces is accounted for via an energy-penalty based wetting (contact-angle) boundary condition. The method is numerically verified by obtaining optimal convergence rates. Several physical validation tests show the robustness and accuracy of the proposed algorithm.