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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37 Citations (Scopus)
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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

Bibliographical note

Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK ‘Octopus’, EPSRC ‘Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents’) and Horizon 2020 ‘In-Vessel Melt Retention’. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC ‘Multi-Scale Exploration of Multi-phase Physics in Flows’. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.


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


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