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Numerical modelling of river flow (numerical schemes for one type of nonconservative systems). (English) Zbl 1426.86004
Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, Dolní Maxov, Czech Republic, June 1–6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 23-36 (2008).
Summary: In this paper, we propose a new numerical scheme to simulate the river flow in the presence of a variable bottom surface. We use the finite volume method, our approach is based on the technique described by D. L. George [Finite volume methods and adaptive refinement for tsunami prop agation and innundation. Seattle, WA: University of Washington (PhD Thesis) (2006)] for shallow water equations. The main goal is to construct the scheme, which is well balanced, i.e., maintains not only some special steady states but all steady states which can occur. Furthermore this should preserve nonnegativity of some quantities, which are essentially nonnegative from their physical fundamental, for example the cross section or depth. Our scheme can be extended to the second order accuracy.
For the entire collection see [Zbl 1194.65013].
86A05 Hydrology, hydrography, oceanography
76M12 Finite volume methods applied to problems in fluid mechanics