Applied Math Seminar Series: Giselle Saylor, Oakland University
Numerical analysis of multiphase flow problems in porous media
Modeling the flow of liquid, aqueous, and vapor phases through porous media is a complex and challenging task that requires solving nonlinear coupled partial differential equations. In this talk, we propose a second-order accurate and energy-stable time discretization method for the three-phase flow problem in porous media. We prove the convergence of the subiterations to resolve the nonlinearity, and show that the time-stepping method mimics the energy balance relation that the continuous problem satisfies. Our spatial discretization uses an interior penalty discontinuous Galerkin method, for which we establish the well-posedness of the discrete problem and provide error estimates under certain conditions on the data. We validate our method through numerical simulations, which show that our approach achieves the expected theoretical convergence rates. Furthermore, the numerical examples highlight the advantages of our time discretization over other time discretizations.
A short bio:
Dr. Giselle Saylor is an Assistant Professor in the Department of Mathematics and Statistics at Oakland University, Michigan. Previously, she was a Postdoctoral Researcher in the Department of Mathematics at the University of Houston where she worked with Dr. Loic Cappanera. In 2020, she obtained her Ph.D. in Applied Mathematics at the University of Waterloo in Canada under the supervision of Dr. Sander Rhebergen.