Simulation of solute transport through fractured rock: A higher-order accurate finite-element finite-volume method permitting large time steps

Stephan K. Matthäi, H. Maghami Nick, Christopher Pain, Insa Neuweiler

Research output: Contribution to journalArticleScientificpeer-review

44 Citations (Scopus)


Discrete-fracture and rock matrix (DFM) modelling necessitates a physically realistic discretisation of the large aspect ratio fractures and the dissected material domains. Using unstructured spatially adaptively refined finite-element meshes, we find that the fastest flow often occurs in the smallest elements. Flow velocity and element size vary over many orders of magnitude, disqualifying global Courant number (CFL)-dependent transport schemes because too many time steps would be necessary to investigate displacements of interest. Here, we present a higher-order accurate implicit pressure-(semi)-implicit transport scheme for the advection-diffusion equation that overcomes this CFL limitation for DFM models. Using operator splitting, we solve the pressure and the transport equations on finite-element, node-centred finite-volume meshes, respectively, using algebraic multigrid methods. We apply this approach to field data-based DFM models where the fracture flow velocity and mesh refinement is 2-4 orders of magnitude greater than that of the matrix. For a global CFL of ≤10,000, this implies sub-CFL, second-order accurate behaviour in the matrix, and super-CFL, at least first-order accurate, transports in fast-flowing fractures. Their greater refinement, however, largely offsets this numerical dispersion, promoting a highly accurate overall solution. Numerical and fracture-related mechanical dispersions are compared in the realistic DFM models using second-order accurate runs as reference cases. With a CFL histogram, we establish target error criteria for CFL overstepping. This analysis indicates that for extreme fracture heterogeneity, only a few transport steps can be sufficient to analyse macro-dispersion. This makes our implicit method attractive for quick analysis of transport properties on multiple realisations of DFM models.

Original languageEnglish
Pages (from-to)289-318
Number of pages30
JournalTransport in Porous Media
Issue number2
Publication statusPublished - 2010
Externally publishedYes


  • DFM
  • DFN
  • Discrete fracture and matrix model
  • Dispersion
  • FEM
  • FVM
  • Hybrid element
  • Passive tracer advection
  • Solute transport
  • Unstructured mesh

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