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On Application of the Weak Galerkin Finite Element Method to a Two-Phase Model for Subsurface Flow

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Abstract

This paper presents studies on applying the novel weak Galerkin finite element method (WGFEM) to a two-phase model for subsurface flow, which couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. The coupled problem is solved in the framework of operator decomposition. Specifically, the Darcy equation is solved by the WGFEM, whereas the saturation is solved by a finite volume method. The numerical velocity obtained from solving the Darcy equation by the WGFEM is locally conservative and has continuous normal components across element interfaces. This ensures accuracy and robustness of the finite volume solver for the saturation equation. Numerical experiments on benchmarks demonstrate that the combined methods can handle very well two-phase flow problems in high-contrast heterogeneous porous media.

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Authors and Affiliations

  1. Department of Mathematics, University of Wyoming, Laramie, WY, 82071, USA

    Victor Ginting

  2. Department of Mathematics, School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA

    Guang Lin

  3. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523-1874, USA

    Jiangguo Liu

Authors
  1. Victor Ginting
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  2. Guang Lin
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  3. Jiangguo Liu
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Correspondence to Jiangguo Liu.

Additional information

V. Ginting was partially supported by US National Science Foundation under Grant DMS-1016283. G. Lin would like to acknowledge support by the Applied Mathematics program of the US DOE Office of Advanced Scientific Computing Research and Pacific Northwest National Laboratory’s Carbon Sequestration Initiative, which is part of the Laboratory Directed Research and Development Program. J. Liu was partially supported by US National Science Foundation under Grant DMS-1419077.

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Ginting, V., Lin, G. & Liu, J. On Application of the Weak Galerkin Finite Element Method to a Two-Phase Model for Subsurface Flow. J Sci Comput 66, 225–239 (2016). https://doi.org/10.1007/s10915-015-0021-8

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  • DOI: https://doi.org/10.1007/s10915-015-0021-8

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