Computational Geosciences

, Volume 19, Issue 2, pp 299–309 | Cite as

Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems

  • Iryna RybakEmail author
  • Jim Magiera
  • Rainer Helmig
  • Christian Rohde


A model formulation to describe fluid flows in coupled saturated/unsaturated porous medium and adjacent free flow regions is proposed. The Stokes equations are applied in the free flow domain, while the Richards equation is used to model the porous medium system. These two flow problems are coupled at the fluid-porous interface via an appropriate set of interface conditions. A multiple-time-step scheme is developed to solve the coupled problem efficiently. Numerical simulation results are presented for a model problem and a realistic setting that demonstrate the convergence and efficiency of the proposed computational algorithm. Time-splitting multistep methods can be successfully applied for modeling other physical systems where the processes evolve on different time scales, and these potential extensions are discussed.


Free flow Porous medium Coupling Stokes equations Richards equation Interface conditions Multiple-time-step method 

Mathematics Subject Classification (2010)

65M99 76D07 76S05 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Iryna Rybak
    • 1
    Email author
  • Jim Magiera
    • 1
  • Rainer Helmig
    • 1
  • Christian Rohde
    • 2
  1. 1.Institute of Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany
  2. 2.Institute for Modelling Hydraulic and Environmental SystemsUniversity of StuttgartStuttgartGermany

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