Transport in Porous Media

, Volume 90, Issue 3, pp 927–947 | Cite as

Operator Splitting Multiscale Finite Volume Element Method for Two-Phase Flow with Capillary Pressure

  • Frederico Furtado
  • Victor Ginting
  • Felipe Pereira
  • Michael Presho


A numerical method used for solving a two-phase flow problem as found in typical oil recovery is investigated in the setting of physics-based two-level operator splitting. The governing equations involve an elliptic differential equation coupled with a parabolic convection-dominated equation which poses a severe restriction for obtaining fully implicit numerical solutions. Furthermore, strong heterogeneity of the porous medium over many length scales adds to the complications for effectively solving the system. One viable approach is to split the system into three sub-systems: the elliptic, the hyperbolic, and the parabolic equation, respectively. In doing so, we allow for the use of appropriate numerical discretization for each type of equation and the careful exchange of information between them. We propose to use the multiscale finite volume element method (MsFVEM) for the elliptic and parabolic equations, and a nonoscillatory difference scheme for the hyperbolic equation. Performance of this procedure is confirmed through several numerical experiments.


Porous media Two-phase flow Multiscale finite volume element method Operator splitting 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Frederico Furtado
    • 1
  • Victor Ginting
    • 1
  • Felipe Pereira
    • 2
  • Michael Presho
    • 3
  1. 1.Department of MathematicsUniversity of WyomingLaramieUSA
  2. 2.Department of Mathematics and School of Energy ResourcesUniversity of WyomingLaramieUSA
  3. 3.Department of MathematicsColorado State UniversityFort CollinsUSA

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