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

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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.

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Authors and Affiliations

  1. Institute for Computational Engineering and Sciences, The University of Texas, 201 East 24th St. Stop C0200, Austin, TX, 78712, USA

    Todd Arbogast, Jamie Pool & Mary F. Wheeler

  2. Department of Mathematics and Systems Analysis, Aalto University School of Science, P.O. Box 11000, FI-00076, Aalto, Finland

    Mika Juntunen

Authors
  1. Todd Arbogast
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  2. Mika Juntunen
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  3. Jamie Pool
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  4. Mary F. Wheeler
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Correspondence to Todd Arbogast.

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Arbogast, T., Juntunen, M., Pool, J. et al. A discontinuous Galerkin method for two-phase flow in a porous medium enforcing H(div) velocityand continuous capillary pressure. Comput Geosci 17, 1055–1078 (2013). https://doi.org/10.1007/s10596-013-9374-y

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  • DOI: https://doi.org/10.1007/s10596-013-9374-y

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