Computational Geosciences

, Volume 17, Issue 6, pp 1055–1078 | Cite as

A discontinuous Galerkin method for two-phase flow in a porous medium enforcing H(div) velocityand continuous capillary pressure

  • Todd Arbogast
  • Mika Juntunen
  • Jamie Pool
  • Mary F. Wheeler
ORIGINAL PAPER

Abstract

We consider the slightly compressible two-phase flow problem in a porous medium with capillary pressure. The problem is solved using the implicit pressure, explicit saturation (IMPES) method, and the convergence is accelerated with iterative coupling of the equations. We use discontinuous Galerkin to discretize both the pressure and saturation equations. We apply two improvements, which are projecting the flux to the mass conservative H(div)-space and penalizing the jump in capillary pressure in the saturation equation. We also discuss the need and use of slope limiters and the choice of primary variables in discretization. The methods are verified with two- and three-dimensional numerical examples. The results show that the modifications stabilize the method and improve the solution.

Keywords

Finite element method FEM Discontinuous Galerkin DG Flow in porous media Capillary pressure IMPES 

Mathematics Subject Classification (2010)

65N30 76S05 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Todd Arbogast
    • 1
  • Mika Juntunen
    • 2
  • Jamie Pool
    • 1
  • Mary F. Wheeler
    • 1
  1. 1.Institute for Computational Engineering and SciencesThe University of TexasAustinUSA
  2. 2.Department of Mathematics and Systems AnalysisAalto University School of ScienceAaltoFinland

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