Computational Geosciences

, Volume 23, Issue 5, pp 881–893 | Cite as

Image-based simulations of absolute permeability with massively parallel pseudo-compressible stabilised finite element solver

  • Liang Yang
  • Jianhui YangEmail author
  • Edo Boek
  • Mikio Sakai
  • Christopher Pain
Original Paper


We apply an accurate parallel stabilised finite element method to solve for Navier-Stokes equations directly on a binarised three-dimensional rock image, obtained by micro-CT imaging. The proposed algorithm has several advantages. First, the linear equal-order finite element space for velocity and pressure is ideal for presenting the pixel images. Second, the algorithm is fully explicit and versatile for describing complex boundary conditions. Third, the fully explicit matrix–free finite element implementation is ideal for parallelism on high-performance computers, similar to lattice Boltzmann. In the last, the memory usage is low compared with lattice Boltzmann or implicit finite volume. We compute the permeability of a range of rock images. The stabilisation parameter may affect the velocity, and an optimal parameter is chosen from the numerical tests. The steady state results are comparable with lattice Boltzmann method and implicit finite volume. The transient behaviour of pseudo-compressible stabilised finite element and lattice Boltzmann method is very similar. Our analysis shows that the stabilised finite element is an accurate and efficient method with low memory cost for the image- based simulations of flow in the pore scale up to 1 billion voxels on 128-GB ram workstation and on distributed clusters.


Stabilised finite element Pore scale Micro-CT image permeability Comparative study Parallel computing 


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Funding information

Liang Yang received financial support from EPSRC grant EP/P013198/1 and Imperial College Research Computing Service [12].


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Water, Energy and Environment (SWEE)Cranfield UniversityBedfordUK
  2. 2.Department of Earth Science and EngineeringImperial College LondonSouth KensingtonUK
  3. 3.Department of Chemical EngineeringImperial College LondonSouth KensingtonUK
  4. 4.Geoscience Research CentreTOTAL E & P UK LimitedWesthillUK
  5. 5.Division of Chemical Engineering & Renewable Energy, School of Engineering and Materials ScienceQueen Mary University of LondonBethnal GreenUK
  6. 6.Resilience Engineering Research Centre, School of EngineeringThe University of TokyoBunkyoJapan

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