Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management

  • Peter Bastian
  • Heiko Berninger
  • Andreas Dedner
  • Christian Engwer
  • Patrick Henning
  • Ralf Kornhuber
  • Dietmar Kröner
  • Mario Ohlberger
  • Oliver Sander
  • Gerd Schiffler
  • Nina Shokina
  • Kathrin Smetana
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)

Abstract

This paper presents recent results of a network project aiming at the modelling and simulation of coupled surface and subsurface flows. In particular, a discontinuous Galerkin method for the shallow water equations has been developed which includes a special treatment of wetting and drying. A robust solver for saturated–unsaturated groundwater flow in homogeneous soil is at hand, which, by domain decomposition techniques, can be reused as a subdomain solver for flow in heterogeneous soil. Coupling of surface and subsurface processes is implemented based on a heterogeneous nonlinear Dirichlet–Neumann method, using the dune-grid-glue module in the numerics software DUNE.

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References

  1. 1.
    Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Kornhuber, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Computing 82(2–3), 121–138 (2008)Google Scholar
  2. 2.
    Bastian, P., Buse, G., Sander, O.: Infrastructure for the coupling of Dune grids. In: Proceedings of ENUMATH, vol. 9, Springer, Berlin Heidelberg (2010)Google Scholar
  3. 3.
    Berninger, H., Kornhuber, R., Sander, O.: Fast and robust numerical solution of the Richards equation in homogeneous soil. SIAM J. Numer. Anal. 49(6), 2576–2597Google Scholar
  4. 4.
    Berninger, H., Kornhuber, R., Sander, O.: Convergence behaviour of Dirichlet–Neumann and Robin methods for a nonlinear transmission problem. In: Proceedings of DD19, LNCSE 78, pp. 87–98. Springer, Berlin (2011)Google Scholar
  5. 5.
    Bunya, S., Dawson, C. et al.: A wetting and drying treatment for the Runge–Kutta DG solution to the shallow water equations. Comput. Meth. Appl. Mech. Eng. 198, 1548–1562 (2009)Google Scholar
  6. 6.
    Dedner, A., Klöfkorn, R.: A generic stabilization approach for higher order Discontinuous Galerkin methods for convection dominated problems. J. Sci. Comp. 10, 1–24 (2010)Google Scholar
  7. 7.
    Dedner, A., Kröner, D., Shokina, N.: Adaptive modelling of two-dimensional shallow water flows with wetting and drying. In: E. Krause, D. Kröner, M. Resch, N. Shokina, Y. Shokin (eds.): Computational Science and High Performance Computing IV, vol. 115, pp. 1–15. Springer (2011)Google Scholar
  8. 8.
    Engwer, C., Sander, O.: A framework for the parallel coupling of Dune grids (in preparation)Google Scholar
  9. 9.
    Helmig, R., Weiss, A., Wohlmuth, B.: Variational inequalities for modeling flow in heterogeneous porous media with entry pressure. Comput. Geosci. 13(3), 373–389 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Peter Bastian
    • 3
  • Heiko Berninger
    • 1
  • Andreas Dedner
    • 2
  • Christian Engwer
    • 3
  • Patrick Henning
    • 4
  • Ralf Kornhuber
    • 1
  • Dietmar Kröner
    • 2
  • Mario Ohlberger
    • 4
  • Oliver Sander
    • 1
  • Gerd Schiffler
    • 5
  • Nina Shokina
    • 2
  • Kathrin Smetana
    • 4
  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany
  2. 2.Abteilung für Angewandte MathematikAlbert-Ludwigs-Universität FreiburgFreiburg i. Br.Germany
  3. 3.Interdisziplinäres Zentrum für Wissenschaftliches RechnenUniversität HeidelbergHeidelbergGermany
  4. 4.Institut für Numerische und Angewandte MathematikUniversität MünsterMünsterGermany
  5. 5.WALD + CORBE GbRHügelsheimGermany

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