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.
Keywords
- Discontinuous Galerkin
- Shallow Water Equation
- Discontinuous Galerkin Method
- Adaptive Modelling
- Richards Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Preview
Unable to display preview. Download preview PDF.
References
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)
Bastian, P., Buse, G., Sander, O.: Infrastructure for the coupling of Dune grids. In: Proceedings of ENUMATH, vol. 9, Springer, Berlin Heidelberg (2010)
Berninger, H., Kornhuber, R., Sander, O.: Fast and robust numerical solution of the Richards equation in homogeneous soil. SIAM J. Numer. Anal. 49(6), 2576–2597
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)
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)
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)
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)
Engwer, C., Sander, O.: A framework for the parallel coupling of Dune grids (in preparation)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bastian, P. et al. (2012). Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management. In: Günther, M., Bartel, A., Brunk, M., Schöps, S., Striebel, M. (eds) Progress in Industrial Mathematics at ECMI 2010. Mathematics in Industry(), vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25100-9_65
Download citation
DOI: https://doi.org/10.1007/978-3-642-25100-9_65
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25099-6
Online ISBN: 978-3-642-25100-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)