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A Method of Lines Flux-Difference Splitting Finite Volume Approach for 1D and 2D River Flow Problems

  • The reliable forecasting of water levels is a very important issue. The modelling approach for water level forecasting at the Middle and Lower River Rhine is based on hydrodynamic river flow models coupled with precipitation-runoff models. The hydrodynamic model is defined by a numerical solution of the one-dimensional (1d) shallow water equations. If flood plains or flood risk maps are important, a two-dimensional (2d) model is required. In this paper the usage of the Alcrudo-Garcia-Navarro scheme (Alcrudo and Garcia-Navarro, 1993) for 1d and 2d problems within the method of lines framework is described. The scheme is slightly modified, in order to allow a more accurate solution of problems with strong variations in the bottom topography. The problem of drying and re-wetting of mesh-cells is not yet fully sufficiently solved. Numerical results for some test problems and an application to a natural river will be presented.

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Document Type:Part of a Book
Author:G. Steinebach, A. Q. T. Ngo
Parent Title (English):Toro (Ed.): Godunov Methods: Theory and Applications
First Page:863
Last Page:871
Publisher:Kluwer Academic/ Plenum Publishers
Place of publication:New York
Publication year:2001
Dewey Decimal Classification (DDC):5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
6 Technik, Medizin, angewandte Wissenschaften / 62 Ingenieurwissenschaften / 627 Wasserbau
Entry in this database:2015/04/02