Riviere, Beatrice2019-05-162019-05-162019-052019-04-17May 2019Liu, Chen. "Discontinuous Galerkin Methods for Pore-scale Multiphase Flow: Theoretical Analysis and Simulation." (2019) Diss., Rice University. <a href="https://hdl.handle.net/1911/105407">https://hdl.handle.net/1911/105407</a>.https://hdl.handle.net/1911/105407In this dissertation, we formulate a pressure-correction projection algorithm, in conjunction with the interior penalty discontinuous Galerkin scheme for time and space discretization to build a single-phase incompressible Navier–Stokes simulator and a two-phase Cahn–Hilliard–Navier–Stokes simulator. The method is a decoupled algorithm, which is especially convenient for large-scale 3D numerical simulations in complex geometry, such as in porous structures obtained from microtomography scanning. The simulators we implemented are robust. The numerical experiment results have been validated on a series of realistic physical problems and exhibit the potential for computing effective properties of single/two-phase flow such as permeability and saturation. Theoretical analysis of the numerical methods for solving multiphase flow model will also contribute to the understanding of the complex multi-scale fluid system from the mathematical point of view. In this dissertation, we also analyze a non-symmetric interior penalty discontinuous Galerkin scheme for solving the mixed form of the Cahn–Hilliard equation and a symmetric interior penalty discontinuous Galerkin scheme for solving the Cahn–Hilliard–Navier–Stokes equations. We prove several numerical properties for these numerical schemes, including unique solvability, stability analysis, and error analysis.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.interior penalty discontinuous GalerkinCahn–Hilliard–Navier–Stokesporous mediaThesis2019-05-16