Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Kröner D.   Dedner A.   Shokina N.  

Adaptive modelling of surface water flows with wetting and drying over complex bottom topographies

Reporter: Shokina N.

     The adaptive modelling of surface water flows over complex bottom topographies with taking into account possible processes of wetting and drying is considered. This work is the continuation of our investigations [6] and has been done under the project “Adaptive Hydrological Modelling with Application in Water Industry” [1] of the Federal Ministry of Education and Research of Germany.
     The two-dimensional shallow water model is used with taking into account the bottom friction and viscosity term in order to move closer to realistic problems. The implementation is done within the DUNE – a modular toolbox for solving partial differential equations with grid-based methods [4].
     The problem is numerically solved by the Runge-Kutta discontinuous Galerkin method [3]. For a correct handling of steady states, a well-balancing method [6] is used, which is based on a reformulation of the topography source term in the balance law for the discharge. In order to handle possible processes of wetting and drying, the wetting-drying treatment, based on the ideas of [2], is incorporated into the model. The newly developed limiter [5] is used for the stabilization of the method. The code is validated on several test problems with known exact solutions and tested on few more complex problems with source, bottom friction and diffusion terms.

2. Bunya S., Kubatko E.J., Westerink J.J., Dawson C. Comput. Methods Appl. Mech. Eng., 198, 1548-1562 (2009)
3. Cockburn B., Shu C.-W. J. Comput. Phys. 141, 199-224 (1998)
5. Dedner A., Klönfkorn R. J. Sci. Comput. DOI: 10.1007/s10915-010-9448-0
6. Dedner A., Kröner D., Shokina N. In: Krause E., Shokin Yu., Resch M., Kröner D., Shokina N. (eds) Computational Science and High Performance Computing IV. Springer Series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design 115, Springer, p. 1-15 (2011)

Abstracts file: dedner_kroener_shokina_NikNik-90.doc
Full text file: dedner_kroener_shokina_NikNik90.pdf

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