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Adaptive modelling of coupled hydrological processes with application in water management. (English) Zbl 1348.76034

Günther, Michael (ed.) et al., Progress in industrial mathematics at ECMI 2010. Proceedings of the 16th European conference on mathematics for industry, Wuppertal, Germany, July 26–30, 2010. Berlin: Springer (ISBN 978-3-642-25099-6/hbk; 978-3-642-25100-9/ebook). Mathematics in Industry 17, 561-567 (2012).
Summary: 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.
For the entire collection see [Zbl 1241.00015].

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q55 NLS equations (nonlinear Schrödinger equations)
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs

Software:

DUNE
PDFBibTeX XMLCite
Full Text: DOI Link

References:

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[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)
[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)
[8] Engwer, C., Sander, O.: A framework for the parallel coupling of Dune grids (in preparation)
[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) · Zbl 1338.76118
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