Adaptive Modelling of Two-Dimensional Shallow Water Flows with Wetting and Drying

  • Andreas Dedner
  • Dietmar Kröner
  • Nina Shokina
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 115)


The current work is done in the framework of the BMBF (Bundesministerium für Bildung und Forschung - the Federal Ministry of Education and Research) project AdaptHydroMod - Adaptive Hydrological Modelling with Application in Water Industry [1], which is devoted to the development of generic adaptive approach to modelling of coupled hydrological processes: surface and groundwater flows. The surface water flow is modelled by the two-dimensional shallow water equations and the surface flow - by the Richards equation. The implementation is based within DUNE - the Distributed and Unified Numerics Environment [14]. The surface flow, on which we focus in the presented paper, is numerically solved using the Runge-Kutta discontinuous Galerkin method [10] with modifications to render the scheme well-balanced and for handling correctly possible wetting and drying processes. The newly developed limiter [12] is used for the stabilization of the method. The validation of the code is done using several test problems with known exact solutions. The problem with a mass source term, which is a first step to the coupled simulation of the surface and groundwater flows, is solved numerically.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andreas Dedner
    • 1
  • Dietmar Kröner
    • 1
  • Nina Shokina
    • 1
  1. 1.Section of Applied MathematicsUniversity of FreiburgFreiburg i. Br.Germany

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