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Nonlinear finite volume method with discrete maximum principle for the two-phase flow model

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Abstract

The discrete maximum principle is a meaningful requirement for numerical schemes used in multiphase flow models. It eliminates numerical pressure overshoots and undershoots, which may cause unnatural Darcy velocities and wrong numerical saturations. In this paper we study the application of the nonlinear finite volume method with discrete maximum principle [1] to the two-phase flow model. The method satisfies the discrete maximum principle for numerical pressures of incompressible fluids with neglected capillary pressure. For non-zero capillary pressure and constant phase viscosities the discrete maximum principle holds for numerical global pressure.

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Authors and Affiliations

  1. Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333, Russia

    K. Nikitin, K. Novikov & Y. Vassilevski

  2. Lomonosov Moscow State University, GSP-1, Moscow, 119991, Russia

    K. Novikov & Y. Vassilevski

  3. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, Moscow oblast, 141700, Russia

    Y. Vassilevski

Authors
  1. K. Nikitin
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  2. K. Novikov
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  3. Y. Vassilevski
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Correspondence to K. Nikitin.

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Submitted by A. V. Lapin

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Nikitin, K., Novikov, K. & Vassilevski, Y. Nonlinear finite volume method with discrete maximum principle for the two-phase flow model. Lobachevskii J Math 37, 570–581 (2016). https://doi.org/10.1134/S1995080216050097

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  • DOI: https://doi.org/10.1134/S1995080216050097

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