Multiscale-stabilized finite element methods for miscible and immiscible flow in porous media

Ruben Juanes*, Tadeusz W. Patzek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In this paper we study the numerical solution of miscible and immiscible flow in porous media, acknowledging that these phenomena entail a multiplicity of scales. The governing equations are conservation laws, which take the form of a linear advection-diffusion equation and the Buckley-Leverett equation, respectively. We are interested in the case of small diffusion, so that the equations are almost hyperbolic. Here we present a stabilized finite element method, which arises from considering a multiscale decomposition of the variable of interest into resolved and unresolved scales. This approach incorporates the effect of the fine (subgrid) scale onto the coarse (grid) scale. The numerical simulations clearly show the potential of the method for solving multiphase compositional flow in porous media. The results for the Buckley-Leverett problem are particularly remarkable.

Original languageEnglish (US)
Pages (from-to)131-140
Number of pages10
JournalJournal of Hydraulic Research
Issue numberEXTRA ISSUE
StatePublished - 2004
Externally publishedYes


  • Conservation laws
  • Finite elements
  • Flow in porous media
  • Multiscale phenomena
  • Stabilized methods

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology


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