A Finite Volume Scheme for Darcy-Brinkman’s Model of Two-Phase Flows in Porous Media

  • Houssein Nasser El Dine
  • Mazen Saad
  • Raafat Talhouk
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


In this paper, we are interested in the displacement of two incompressible phases in a Darcy-Brinkman flow in a porous media. The equations are obtained by the conservation of the mass and by considering the Brinkman regularization velocity of each phase. This model is treated in its general form with the whole nonlinear terms. This paper deals with construction and convergence analysis of a finite volume scheme together with a phase-by-phase upstream according to the total velocity. Finally, numerical tests illustrate the behavior of the solutions of this proposed scheme.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Houssein Nasser El Dine
    • 1
    • 2
  • Mazen Saad
    • 1
  • Raafat Talhouk
    • 2
  1. 1.École Centrale de Nantes. UMR 6629 CNRS, Laboratoire de Mathématiques Jean LerayNantesFrance
  2. 2.Doctoral School of Sciences and Technology (EDST), Laboratory of MathematicsLebanese UniversityBeirut, HadathLebanon

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