Discontinuous Galerkin Methods Applied to Two-Phase ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Discontinuous Galerkin Methods Applied to Two-Phase Flow Problems
Paper
Author:Owen Eslinger <owen.j.eslinger@erdc.usace.army.mil> (ERDC)
Mary Wheeler <mfw@ices.utexas.edu> (The University of Texas at Austin)
Presenter:Owen Eslinger <owen.j.eslinger@erdc.usace.army.mil> (ERDC)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000465
DOI:10.4122/1.1000000466

A set of discontinuous Galerkin (DG) finite element methods are proposed to solve the two-phase flow equations, such as the air-water system that arises in shallow subsurface flow problems. The two time-splitting approaches detailed incorporate primal formulations, such as the Oden-Baumann-Babuska DG (OBB-DG), Symmetric Interior Penalty Galerkin (SIPG), Non-Symmetric Interior Penalty Galerkin (NIPG), and Incomplete Interior Penalty Galerkin (IIPG), as well as a local discontinuous Galerkin (LDG) method applied to the saturation equation. The two-phase flow equations presented are split into sequential and implicit pressure/explicit saturation (IMPES) formulations. The IMPES formulation introduced in this work uses a primal DG formulation to solve the pressure equation implicitly at every time step, and then uses an explicit LDG scheme for saturation equation. The LDG scheme employed advances in time via explicit Runge-Kutta time stepping, while employing a Kirchoff transformation for the local solution of the degenerate diffusion term. DG finite element methods are naturally suited to problems subsurface flow and transport. They can handle general meshes which may be non-conforming, they can treat higher order approximations, and they are locally mass conservative, among many other desirable properties. In particular, due to different rock properties at the interface between two materials, fluid saturations may be discontinuous. Therefore DG methods are a natural fit for this class of problems. Computational results showing that the IMPES method proposed will hold capillary barriers while using two capillary pressure curves in different materials are presented.