A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

J.L.M.A. Gomes, D Pavlidis, P Salinas, Z Xie, J. R. Percival, Y. Melnikova, C. C. Pain, M. D. Jackson

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A novel method for simulating multi-phase flow in porous media is presented. The approach is based on a control volume finite element mixed formulation and new force-balanced finite element pairs. The novelty of the method lies in: (a) permitting both continuous and discontinuous description of pressure and saturation between elements; (b) the use of arbitrarily high-order polynomial representation for pressure and velocity and (c) the use of high-order flux-limited methods in space and time to avoid introducing non-physical oscillations while achieving high-order accuracy where and when possible. The model is initially validated for two-phase flow. Results are in good agreement with analytically obtained solutions and experimental results. The potential of this method is demonstrated by simulating flow in a realistic geometry composed of highly permeable meandering channels.
Original languageEnglish
Pages (from-to)431–445
Number of pages23
JournalInternational Journal for Numerical Methods in Fluids
Issue number5
Early online date4 Aug 2016
Publication statusPublished - 20 Feb 2017



  • CVFEM mixed formulation
  • discontinuous Galerkin
  • flux-limiting
  • high-order method
  • multi-phase flows
  • porous media flows

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