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Monotonicity for MPFA methods on triangular grids

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Abstract

Flow in a porous medium can be described by a set of non-linear partial differential equations. The pressure variable satisfies a maximum principle, which guarantees that the solution will have no oscillations. A discretisation of the pressure equation should preserve this monotonicity property. Whether a numerical method is monotone will depend both on the medium and on the grid. We study monotonicity of Multi-point Flux Approximation methods on triangular grids. We derive necessary conditions for monotonicity on uniform grids. Further, we study the robustness of the methods on rough grids, and quantify the violations of the maximum principle. These investigations are done for single phase flow, however, they are supported by two-phase simulations.

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Authors and Affiliations

  1. Centre for Integrated Petroleum Research (CIPR), UiB, Department of Mathematics, University of Bergen (UiB), P.O. Box 7800, 5020, Bergen, Norway

    Eirik Keilegavlen

  2. CIPR, Bergen, Norway

    Ivar Aavatsmark

Authors
  1. Eirik Keilegavlen
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  2. Ivar Aavatsmark
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Correspondence to Eirik Keilegavlen.

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Keilegavlen, E., Aavatsmark, I. Monotonicity for MPFA methods on triangular grids. Comput Geosci 15, 3–16 (2011). https://doi.org/10.1007/s10596-010-9191-5

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  • DOI: https://doi.org/10.1007/s10596-010-9191-5

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