Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

Kirill M. Gerke, Roman V. Vasilyev, Siarhei Khirevich, Daniel Collins, Marina V. Karsanina, Timofey O. Sizonenko, Dmitry V. Korost, Sébastien Lamontagne, Dirk Mallants

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.
Original languageEnglish (US)
Pages (from-to)41-58
Number of pages18
JournalComputers & Geosciences
StatePublished - Jan 17 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We are grateful to Brendan Speet (CSIRO Land and Water) for his help with the computational resources. We also thank Prof. Vladimir Voevodin for providing computational resources of Moscow State University Computational Centre. Collaborative effort of the authors is within FaT iMP (Flow and Transport in Media with Pores) research group ( K.M.G., R.V.V, M.V.K., D.V.K., T.O.S. were supported by Russian Science Foundation grant 14-17-00658 (X-ray microtomography), while K.M.G., M.V.K., T.O.S. were also supported by Russian Science Foundation grant 17-17-01310 (pore-scale simulations).


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