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Numerical analysis for two-phase flow with non-equilibrium capillary pressure in anisotropic porous media

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Abstract

In this paper, we are concerned with the convergence analysis of a combined finite volume-non-conforming finite element scheme, to approximate the two incompressible phase flow with dynamic capillary pressure in anisotropic porous media. All diffusion terms are anisotropic and heterogeneous and they are discretized by piecewise linear non-conforming triangular finite elements whereas the mobilities are discretized on dual diamond mesh. The mobilities are approximated by a non-standard way considering the inverse of the mean value of the inverse of mobilities across the interface of the dual mesh. This approximation ensures a priori estimates on the global pressure and on the water saturation. Under the assumption of non-degeneracry of mobilities, we prove the convergence of the combined scheme for the complete two-phase flow including the non-equilibrium capillary pressure.

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Funding

The second and the fourth authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this research through research group no. (RG- 1440-118).

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Authors and Affiliations

  1. Faculté des Sciences, Département de Mathématiques et Informatique, Université Dr. Yahia Feres de Médéa, Médéa, 26000, Algérie

    Khaled Bouadjila

  2. Department of Biomedical Technology, College of Applied Medical Sciences, King Saud University, P.O.Box 10219, Riyadh, 11433, Saudi Arabia

    Ali Samir Saad & Wissal Mesfar

  3. École Centrale de Nantes, Laboratoire de Mathématiques Jean Leray, UMR 6629 CNRS. 1 rue de la Noé, F-44321, Nantes, France

    Mazen Saad

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  1. Khaled Bouadjila
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  2. Ali Samir Saad
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Correspondence to Mazen Saad.

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Communicated by: Aihui Zhou

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Bouadjila, K., Saad, A.S., Saad, M. et al. Numerical analysis for two-phase flow with non-equilibrium capillary pressure in anisotropic porous media. Adv Comput Math 48, 56 (2022). https://doi.org/10.1007/s10444-022-09972-0

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