Validation and calibration of coupled porous-medium and free-flow problems using pore-scale resolved models


The correct choice of interface conditions and effective parameters for coupled macroscale free-flow and porous-medium models is crucial for a complete mathematical description of the problem under consideration and for accurate numerical simulation of applications. We consider single-fluid-phase systems described by the Stokes–Darcy model. Different sets of coupling conditions for this model are available. However, the choice of these conditions and effective model parameters is often arbitrary. We use large-scale lattice Boltzmann simulations to validate coupling conditions by comparison of the macroscale simulations against pore-scale resolved models. We analyse three settings (lid-driven cavity over a porous bed, infiltration problem and general filtration problem) with different geometrical configurations (channelised and staggered distributions of solid grains) and different sets of interface conditions. Effective parameters for the macroscale models (permeability tensor, boundary layer constants) are computed numerically for each geometrical configuration. Numerical simulation results demonstrate the sensitivity of the coupled Stokes–Darcy problem to the location of the sharp fluid–porous interface, the effective model parameters and the interface conditions.


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Open Access funding provided by Projekt DEAL. The authors thank Ivan Yotov, Jim Magiera and Christoph Rettinger for the valuable discussions. The authors are grateful to the Regionales Rechenzentrum Erlangen ( for providing access to supercomputing facilities.


I. Rybak and E. Eggenweiler received financial support for this work from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) by funding SFB 1313, Project Number 327154368. C. Schwarzmeier and U. Rüde received funding from the DFG for supporting project RU 422/27 and the Bundesministerium für Bildung und Forschung (BMBF, Federal Ministry of Education and Research) for supporting the projects HPC2SE (01ICH16003D) and SKAMPY (01IH15003A).

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Rybak, I., Schwarzmeier, C., Eggenweiler, E. et al. Validation and calibration of coupled porous-medium and free-flow problems using pore-scale resolved models. Comput Geosci (2020).

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  • Stokes equations
  • Darcy’s law
  • Interface conditions
  • Lattice Boltzmann method

Mathematics Subject Classification (2010)

  • 68N99
  • 76D07
  • 76M50
  • 76S05