期刊
ADVANCES IN WATER RESOURCES
卷 34, 期 8, 页码 980-989出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.advwatres.2011.05.002
关键词
Shallow water system; Exner equation; Sediment transport; Hyperbolicity; Stability; Splitting methods
资金
- project METHODE [ANR-07-BLAN-0232]
- Spanish Government [MTM2009-11293]
- Agence Nationale de la Recherche (ANR) [ANR-07-BLAN-0232] Funding Source: Agence Nationale de la Recherche (ANR)
In this paper, we are concerned with sediment transport models consisting of a shallow water system coupled with the so called Exner equation to describe the evolution of the topography. We show that, for some bedload transport models like the well-known Meyer-Peter and Muller model, the system is hyperbolic and, thus, linearly stable, only under some constraint on the velocity. In practical situations, this condition is hopefully fulfilled. Numerical approximations of such system are often based on a splitting method, solving first shallow water equation on a time step and, updating afterwards the topography. It is shown that this strategy can create spurious/unphysical oscillations which are related to the study of hyperbolicity. Using an upper bound of the largest eigenvector may improve the results although the instabilities cannot be always avoided, e.g. in supercritical regions. (C) 2011 Elsevier Ltd. All rights reserved.
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