Discontinuous approximation of viscous two-phase flow in heterogeneous porous media

Raimund Bürger, Sarvesh Kumar, Kenettinkara Sudarshan Kumar, Ricardo Ruiz-Baier

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13 Citations (Scopus)


Runge-Kutta Discontinuous Galerkin (RKDG) and Discontinuous Finite Volume Element (DFVE) methods are applied to a coupled flow-transport problem describing the immiscible displacement of a viscous incompressible fluid in a non-homogeneous porous medium. The model problem consists of nonlinear pressure-velocity equations (assuming Brinkman flow) coupled to a nonlinear hyperbolic equation governing the mass balance (saturation equation). The mass conservation properties inherent to finite volume-based methods motivate a DFVE scheme for the approximation of the Brinkman flow in combination with a RKDG method for the spatio-temporal discretization of the saturation equation. The stability of the uncoupled schemes for the flow and for the saturation equations is analyzed, and several numerical experiments illustrate the robustness of the numerical method.

Original languageEnglish
Pages (from-to)126-150
Number of pages25
JournalJournal of Computational Physics
Publication statusPublished - 15 Sept 2016
Externally publishedYes


  • Brinkman equations
  • Discontinuous fluxes
  • Finite volume element methods
  • Runge-Kutta discontinuous Galerkin methods
  • Stabilization
  • Two phase flow

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